Search

This paper proposes a novel procedure for discretizing uncertain time-invariant continuous-time linear systems in polytopic domains. The approach is based on multistep method theory and involves mixing models obtained with different multiples of a fixed step-size (sampling time), thereby increasing data availability. An optimization procedure is employed to determine the coefficients that minimize the residual discretization error, and then these coefficients are combined to construct an augmented structure for the discrete-time system. The discretization error is computed using a grid search and incorporated into the discrete-time system formulation. Using the resulting discrete-time system, a state feedback methodology is applied to synthesize digital controllers capable of stabilizing the original continuous-time system. The paper presents two sufficient Linear Matrix Inequality (LMI)-based conditions for designing robust controllers specific to the proposed structure. The first condition utilizes a constant Lyapunov function, while the second condition employs a parameter-dependent Lyapunov function. In both cases, the proposed conditions guarantee asymptotic stability for the continuous-time system in closed-loop. A numerical experiment is conducted to illustrate the validity and effectiveness of the proposed method. • Discretizatizing continuous-time time-invariant uncertain systems is an open problem. • Considering delayed steps in the discretization can provide more information. • Suitable discrete-time control design procedures are presented. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the dynamic feedback design for linear systems with input disturbance. We propose a new approach to design dynamic feedback such that the disturbance in the control channel can be compensated effectively. An interesting characteristic about the disturbance robustness of dynamic feedback is found. Thanks to this interesting characteristic, we just need to consider the disturbance-free system to make the dynamic feedback design. This fact is well validated by several dynamic feedback laws proposed in this paper. Our results are available for the regular linear system with harmonic disturbance. Moreover, the stabilization of an unstable heat equation with general periodic disturbance is also investigated. In order to validate the theoretical results visually, some numerical simulations are given to show the effectiveness of the proposed dynamic feedback. [ABSTRACT FROM AUTHOR]

This paper considers leader–follower consensus of linear multiagent systems with unknown inputs. The proposed technical framework consists of two processes, that is, estimation and control. For the estimation process, we design a complementary sector region based on a novel reset variable. In this region, a class of distributed extended state observers that depends on the above variables is constructed, which completes the estimation of system states and unknown inputs, simultaneously. This reset strategy also guarantees that the system states are quickly estimated. For the control process, the distributed output feedback controller associated with the reset strategy is designed. The unknown input is also compensated under the reset strategy, which achieves the objective of consensus. Finally, effectiveness of the presented method is validated by an example. [ABSTRACT FROM AUTHOR]

This paper proposes the hierarchical stability conditions for linear systems with an interval time-varying delay. In the matter of the delay, the upper and lower bounds are restricted, but there is no constraint on its derivative. Firstly, based on the state vectors and multiple integral state vectors involved in the delay-related generalized free-matrix-based integral inequalities (GFIIs), the hierarchical Lyapunov-Krasovskii functional (LKF) candidates are constructed. Then, the GFIIs are applied for the approximation of the integral quadratic terms, which will introduce the delay related nonlinear terms in the LKF differential. Next, the novel adjusted matrix-valued high and odd degree polynomial negative definite conditions (NDCs) are provided to acquire the hierarchical linear matrix inequality (LMI) conditions and cope with the nonlinear terms introduced by the GFIIs. Eventually, the advantages of the obtained stability conditions are checked through some numeric examples. [ABSTRACT FROM AUTHOR]

In this paper, some techniques are proposed to determine the smallest perturbation that causes the loss of a structural property for a linear system with coefficients depending polynomially on a vector of parameters. In the case that the interest lies on a single structural property, the analysis is carried out using directly the state-space description of the system, whereas, in the case that the interest is to characterize either the pair (reachability and observability) or the pair (stabilizability and detectability), the analysis is carried out using the transfer matrix of the plant. Examples of application of the proposed methods are reported all throughout the paper to illustrate and validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with model predictive control (MPC) for multisensor linear systems. In order to fully utilize information and achieve higher control accuracy, two fusion MPC algorithms are proposed. The first algorithm is named estimation-fusion model predictive controller (E-F MPC), which local estimations are fused and then fusion control input is obtained by the fusion estimation. The second algorithm is named control-fusion model predictive controller (C-F MPC), which fuses the control inputs obtained from local systems. The relationships, differences and complexity of the two algorithms are analyzed. The advantages of E-F MPC are that it is simple and easy to implement with high control accuracy, while the disadvantage is the bad robustness because of the heavy estimation, prediction and control tasks for the fusion node. For C-F MPC, with a small loss of accuracy, network throughput and computational cost of its fusion node will be greatly reduced, which makes it good robustness and flexibility. Simulation analysis verifies the effectiveness and correctness of the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, the problem of power efficiency evaluation for n -ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class. • Power efficiency modeling and efficiency maps computation for physical systems. • Interchangeable efficiency maps computed on the different systems energetic ports. • Highlighting of intrinsic properties and of a design parameter for two-ports systems. • Efficiency maps computation and intrinsic characteristics of planetary gear sets. [ABSTRACT FROM AUTHOR]

This paper concentrates on the stability analysis of linear systems with a time-varying delay. Firstly, a new Lyapunov–Krasovskii functional (LKF) is given, which involves more time delay cross-terms information. Secondly, an improved reciprocally convex inequality with higher estimation accuracy is derived. Then, on the basis of the constructed LKF and the improved reciprocally convex inequality, some new stability criteria with less conservative are proposed. Finally, the superiority of the obtained stability criteria is explained by two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments. [ABSTRACT FROM AUTHOR]

This paper systematically investigates consensus tracking of linear multi-agent systems with disturbances over directed switching topologies. Both state and output feedback H ∞ controllers are jointly synthesized with the triggering mechanism. First, a state-based event-triggered H ∞ controller design for achieving consensus tracking is carried out, which can result in settling the occurrence of disturbances and the reduction of controller updates as well as averting Zeno behavior. Considering the case that only output information of agent is required, an event-triggered H ∞ output feedback controller is then proposed and sufficient condition for the solvability of consensus tracking problem are also derived. Compared with the existing results, the effects of disturbances on directed switching topologies can be tackled when continuous communication and full-state information of the agent are not needed. Numerical simulation are finally conducted to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the leader-following consensus problem for general linear multiagent systems under a fully distributed manner. To avoid using the global information of the communication network, two node-based adaptive parameters are designed and introduced to the fully distributed event-based control law. Such a protocol is more scalable and flexible for large-scaled and complex networked system, such as microgrids or multiple unmanned vehicles. A novel event-triggered rule is presented, and an internal dynamic variable is introduced in it to further cut down the triggering times and save the communication resources. A well-designed Lyapunov function candidate is constructed to not only ensure the convergence of the close-looped systems but also avoid using the eigenvalue of Laplacian matrix in the dynamic variable. Moreover, it is proved that the designed event-triggered conditions can avoid the Zeno behaviour. Finally, a simulation example based on a group of unmanned intelligent vehicle systems is provided to demonstrate the validity of the designed control method. [ABSTRACT FROM AUTHOR]

Theoretical developments in the field of superconducting microwave circuits involving continuous measurement feedback control as well as coherent feedback control are essential for advances in the domain of quantum technology. The smallest structures that can be fabricated by lithographic technologies request the inevitable development of the quantum control theory in order for quantum systems to function reliably in an engineering sense. Within these perspectives, this paper develops the positive real properties for a class of quantum systems involving annihilation operators only and then relates them to the corresponding bounded real properties and consequently to physical realizability conditions developed earlier by the authors. Based on these positive real properties of the annihilation operators quantum systems, it is shown that it is possible to use the Brune algorithm in order to find electrical circuits that can physically implement the type of quantum systems involving annihilation operators only. This would involve Josephson junctions, microwave cavities, and voltage sources. This theory, illustrated for one-port circuits, is essential for the implementation of microwave circuits especially those related to quantum filters found in the field of quantum computing. [ABSTRACT FROM AUTHOR]

In this paper, a robust H ∞ analysis method is presented for a class of uncertain quantum systems where uncertainties may exist in the system and interaction Hamiltonians, and the coupling operators. We provide a sufficient condition to guarantee this class of uncertain systems robust strictly bounded real with respect to a given disturbance attenuation. Moreover, we propose a robust H ∞ control method for quantum systems with uncertain system Hamiltonian and uncertain coupling operators. The controller and the quantum plant are connected via direct and indirect couplings. This robust H ∞ control problem is shown to have a connection with a scaled H ∞ problem. We propose a numerical procedure to find the corresponding coefficients of the desired H ∞ controller by using an LMI formulation and multi-step optimization. [ABSTRACT FROM AUTHOR]

In this paper, the exponential function is firstly defined for con-matrices, and some elegant properties are provided. With the exponential function as a tool, the state response of a con-number-valued system is obtained. The concept of controllability for ordinary linear systems is also extended to the case of con-number-valued systems, and a criterion is also provided according to the original coefficient con-matrices for the controllability. In addition, an example of four cavities interacting with each other by two nonlinear crystals is presented to illustrate the theoretical superiority of con-numbered-value systems. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive event-triggered control for semi-Markovian jump linear systems with process time-varying delays. For reducing the data transmission amount from the sensor-to-controller, a switching-mode dependent adaptive event-trigger (AET) is proposed wherein a positive auxiliary function is involved. Utilizing the received non-periodical state information, a switching state feedback control law is investigated. By aid of an exponential inequality technique, the controller design method is conveniently presented. The proposed control method not only guarantees the globally exponentially stability of the closed-loop system but also is capable of regulating the decay rate. An approximation approach for the minimal event-triggered time-interval of the AET is given as well. It has been proved that the unwanted Zeno behavior will not exhibit. The proposed control method is employed to a transmission control protocol based active queue management (TCP/AQM) system and the numerical experiment demonstrates its effectiveness. [ABSTRACT FROM AUTHOR]

Due to the time-varying nature of time-varying linear systems, many traditional time-invariant methods cannot solve time-varying linear systems. The emergence of zeroing neural networks (ZNN) has led to a long and intensive development in this field. Researchers have mainly studied or improved the ZNN model for time-varying linear systems in the direction of activation functions and design parameters. This paper proposes a novel modified versatile activation function (MVAF) from the perspective of activation function optimization, and a modified versatile activation function zeroing neural network (MVAFZNN) model for solving time-varying generalized linear matrix equations is constructed. The proposed model converges faster than the versatile activation function zeroing neural network (VAFZNN) model and other ZNN models. Theoretical analysis shows that the MVAFZNN model can solve time-varying systems in a predetermined time. Two numerical experiments verify the validity of the proposed model, and two circuit experiments show that the proposed model can be used to calculate circuit parameters. [ABSTRACT FROM AUTHOR]

Stabilisation of asynchronous switching semi-Markovian jump stochastic systems is discussed in this paper. By the ergodic property of the semi-Markov process and the method of multiple Lyapunov functions, some sufficient conditions for almost sure exponential stability of stochastic systems are formulated, which cover some existing results in the literature. Applications of the obtained results to two special types of systems are then reformulated in a more convenient way. In particular, the non-equally dividing technique is used to construct solvable conditions for asynchronous semi-Markovian jump linear stochastic systems. Numerical examples are performed to verify the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of sensor fault detection (FD) for discrete-time linear systems. First, considering the influence of disturbance, an adaptive law is designed based on the interval observer theory, which can effectively compress the error interval of output estimation, and improve the sensitivity to sudden faults. Then, based on adaptive interval observer (AIO), a flexible event-triggering fault detection mechanism is designed. Different from the existing methods, the event-triggering condition has greater flexibility. At the same time, the adaptive law can ensure that the zero signal belongs to the upper and lower bound of residual. Based on the robustness theory, the linear matrix inequality conditions (LMIs) satisfying the H ∞ performance index are derived. Finally, the effectiveness of the proposed method is demonstrated by an aeroengine simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates dynamic event-triggered adaptive leader-following semi-global bipartite consensus (SGBC) of multi-agent systems (MASs) with input saturation. A dynamic event-triggered adaptive control (DETAC) protocol is presented, where the triggering function can regulate its threshold value dynamically. It's turned out that the SGBC can be achieved via the DETAC protocol under some inequalities. Then, the proposed DETAC protocol is extended to solve bipartite consensus under jointly connected topology. Furthermore, the Zeno behaviors will be avoided. Finally, the rationality of proposed DETAC protocols are tested by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, a two-layer supervisory control scheme is proposed for discrete-time linear systems with state/input constraints, including multiple state time-delays, parametric uncertainties, and exogenous disturbance. The inner control layer is designed to achieve robust H ∞ tracking performance considering the delays as extra states but neglecting the input/state constraints. On the other hand, in the outer control layer, a command governor (CG) is designed to robustly guarantee the satisfaction of state and input constraints by computing a minimal Robust Positively Invariant (mRPI). To this end, the CG manipulates reference inputs by generating the nearest admissible value to be applied to the closed-loop system in both transient and steady-state response through the computation of the Maximal Output Admissible Set (MOAS). Finally, the validity of the proposed scheme is assessed in simulation using a numerical example and a continuous stirred tank reactor (CSTR) system. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic event-based resilient consensus control of the multiple networked Euler-Lagrangian (E-L) systems under the Denial of Service (DoS) attacks is considered. Compared with linear cyber-physical systems, nonlinear networked E-L systems are more complex and closer to actual mechanical systems. For the situation where the topology is a strongly connected directed topology, a controller based on a dynamic event-trigger mechanism is designed to achieve consensus control for the networked E-L system in the absence of DoS attacks. Sufficient conditions are presented, which can guarantee the closed-loop system be stable. Then the resilient consensus problem of event-based controllers under energy-constrained DoS attacks is analyzed. The conditions related to the duration and frequency of DoS attacks are given. Zeno behavior is proved does not exist in the proposed control scheme. Finally, some numerical simulation results are given for verifying the theoretical results. [ABSTRACT FROM AUTHOR]

• Interval state estimation problem for continuous-time positive linear systems under intermittent denial-of-service (DoS) attacks is considered. • Two types of interval estimation strategies are proposed. • Conditions ensuring the interval estimation of each strategy are derived using mode-dependent Lyapunov method. This paper is concerned with the interval state estimation problem for continuous-time positive linear systems under intermittent denial-of-service (DoS) attacks. To solve the problem, two types of estimate strategies are proposed. One is using the interval observer at all times, the other is using the interval observer in the absence of attacks but using, instead, the interval predictor otherwise. To facilitate the analysis, the interval state estimation problem is reformulated into the positivity and stability analysis of the associated error system. Then, stability conditions and disturbance attenuation characterization of the error systems for the two strategies are established via a mode-dependent Lyapunov approach. Roughly speaking, it is shown that the interval estimation accuracy of the former strategy is higher than the latter when the open loop system is stable. Finally, several numerical examples are provided to illustrate the ascendancy of the proposed estimation strategies. [ABSTRACT FROM AUTHOR]

Networked systems using redundant channels to transmit data can effectively reduce the probability of data loss and improve system reliability and control margin. However, the structural complexity and economic cost of the system are also increased. To balance the redundancy and feasibility, the ratio of attraction domain to packet loss rate is defined as a balanced feasibility index. In this paper, single-channel packet loss is considered as Bernoulli distribution and a bounded packet loss network system control model is constructed as the arbitrary bounded packet loss control problem for redundant channel transmission network system. Therefore, the robust conditions of the closed-loop system and the constraints of the input and state are established under the framework of robust predictive control to construct the linear matrix inequality (LMI) optimization problem. Finally, to verify the effectiveness of the design method proposed in this paper, the discrete time-varying linear system and the main steam control system with redundant channels are used as study cases. [ABSTRACT FROM AUTHOR]

In this paper, a sliding mode sensor fault tolerant control scheme which involves a first order sliding mode observer, fault compensation logic and an integral sliding mode controller, is proposed for a class of uncertain linear parameter-varying systems. The proposed scheme has the capability to retain near nominal fault-free performance in the face of a class of sensor faults/failures. In particular, the closed-loop stability of the sensor fault tolerant scheme involving the sliding mode observer and the sliding mode controller in the presence of faults and uncertainty, is rigorously analysed. Furthermore, the paper proposes an algorithm to simultaneously synthesize the design freedom associated with the observer gains and control law despite the lack of a separation principle in the closed loop system overall caused by the uncertainty. The proposed scheme is validated using a commercial aircraft model. Good simulation results show the efficacy of the scheme. [ABSTRACT FROM AUTHOR]

This paper studies almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control. New expectation-based sufficient conditions for almost sure exponential stability of the system are derived by employing the coupled Lyapunov function related to the sojourn time and the ergodic property of semi-Markov chains. Compared with known results on almost sure exponential stability of discrete-time semi-Markovian linear systems, the results in this paper are shown to be less conservative. At last, three numerical examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

In today's information era, cyber–physical systems (CPS) have been widely used in many industrial and infrastructure fields, and the study of security problems of CPS has become a crucial issue. For linear discrete-time systems, this paper investigates the state estimation problem based on the quantized innovations and transmission data tampering scenarios. From the attacker's view, by designing the tampering matrix and combining the property of the error function, the optimal attack strategy in the sense of maximizing the prediction error covariance matrix is given. From the defender's view, the optimal defense scheme based on multiplicative compensation is given in the case of a known attack strategy. Moreover, in the case of unknown attack strategies, a joint estimation algorithm is designed to give the optimal defense scheme subject to error constraints. In this paper, state estimators in recursive form are given for all above cases, and the algorithms are proved to be consistent. The theoretical results obtained are verified by simulations. • The recursive algorithms of state updating for system with quantized observations under data tampering attack. • Asymptotic performance of modified algebraic Riccati equation (MARE). • The optimal attack strategy in tampering transmission data to maximize hit impact. • A novel joint estimation approach to minimize attack impact when the attack strategy is known and unknown. • The optimal defense scheme to reach a balance between attack strategy estimations and the state estimation covariance matrix. [ABSTRACT FROM AUTHOR]

• New scenario-based MPC strategy developed for linear systems subject to correlated parametric and/or additive uncertainties. • The proposed algorithm adapts the conditional scenario reduction method to the MPC framework. • Two numerical examples validate the higher probability of constraint satisfaction of the proposed MPC. • The high probability of constraint satisfaction of the proposed MPC allows solving a OCP with fewer scenarios when a shorter solution time is needed. This paper proposes a novel MPC approach called conditional scenario-based model predictive control (CSB-MPC), developed for discrete-time linear systems affected by parametric uncertainties and/or additive disturbances, which are correlated and with bounded support. At each control period, a primary set of equiprobable scenarios is generated and subsequently approximated to a new reduced set of conditional scenarios in which each has its respective probabilities of occurrence. This new set is considered for solving an optimal control problem in whose cost function the predicted states and inputs are penalised according to the probabilities associated with the uncertainties on which they depend in order to give more importance to predictions that involve realisations with a higher probability of occurrence. The performances of this new approach and those of a standard scenario-based MPC are compared through two numerical examples, and the results show greater probabilities of not transgressing the state constraints by the former, even when considering a smaller number of scenarios than the scenario-based MPC. [ABSTRACT FROM AUTHOR]

This paper investigates the event-based consensus problems for linear multi-agent systems under directed network topology. First, a new event-triggered control method is proposed for the leader-following consensus problem of agents under directed graphs. Then this new method is applied to the cluster control problem under special topological conditions. The new event-based control scheme is better than some existing literature in the following aspects. 1) The graph only needs to contain a spanning tree instead of being required to be strongly connected graph or undirected, and the triggering function is state-dependent rather than time-dependent. 2) Some parameters are designable for the trade-off between the event interval and the performance of the controlled system. Besides, the optimization of some parameters is studied to reduce the trigger frequency. All the agents can achieve consensus with an exponential speed when communications among follower agents are intermittent, and Zeno behavior is excluded under the proposed method. 3) When applying this method to the cluster control problem, agents in the same cluster share the same form of triggering function. Cluster consensus can be achieved regardless of intra- and inter-cluster relative coupling strength under the event-triggered control framework. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of set-based finite-time stability (SFTS) and set-based finite-time boundedness (SFTB) for both certain and uncertain linear time-varying systems. The concepts of SFTS and SFTB are defined. Different from existing results, sufficient conditions for SFTS and SFTB are directly derived from the basic definitions of finite-time stability (FTS) and finite-time boundedness (FTB) by using the convex hull technique rather than utilizing the weighted quadratic functions. Thus, more practical constraints on the system states can be dealt with. Furthermore, intervals, zonotopes and polytopes are employed to describe the typical compact convex sets. For linear uncertain systems, the uncertain time-varying state sets are assumed to be represented by interval matrices and matrix zonotopes, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

This paper considers the finite-time bipartite consensus problem governed by linear multiagent systems subject to input saturation under directed interaction topology. Due to the existence of input saturation, the dynamic performance of linear multiagent systems degrades significantly. For the improvement of the dynamic performance of systems, a dynamic gain scheduling control approach is proposed to design a dynamic Laplacian-like feedback controller, which can be obtained from the analytical solution of a parametric Lyapunov equation. Suppose that each agent is asymptotically null controllable with bounded control, and that the corresponding interaction topology of the signed directed graph with a spanning tree is structurally balanced. Then the dynamic Laplacian-like feedback control can ensure that linear multiagent systems will achieve the finite time bipartite consensus. The dynamic gain scheduling control can better improve the bipartite consensus performance of the linear multiagent systems than the static gain scheduling control. Finally, two examples are provided to show the effectiveness of the proposed control design method. [ABSTRACT FROM AUTHOR]

This paper presents explicit and implicit discrete-time realizations for the robust exact filtering differentiator , aiming to facilitate an adequate posterior implementation structure in digital devices. This paper firstly presents an analysis of an explicit discrete-time realization of the filtering differentiator based on linear systems' exact discretization with a zero-order holder. For this case, however, high-order terms in the filter dynamics may cause instability of the estimation error for signals with unbounded derivatives. Hence, two other new discrete-time realizations of the filtering differentiator are derived by removing some high-order terms in the filter dynamics. The first one is an explicit discrete-time realization, while the second one is implicit. After a finite time, both preserve the accuracy of the continuous-time robust exact filtering differentiator in the presence of measurement noise. For each proposed discrete-time scheme, a stability analysis based on homogeneity is provided. Finally, the simulation results include comparisons between the proposed implicit and explicit discrete-time realizations with other existing schemes. These numerical studies highlight that the implicit scheme supersedes the explicit one, consistent with the implicit and explicit realizations of other continuous-time algorithms. [ABSTRACT FROM AUTHOR]

• The control problem of a non-linear MIMO wave equation is considered. • To get the optimal control of the PDE, a repetitive process is used, and the applied method is based on the ILC. • Not like almost of the ILC algorithm, the initial condition here also has an iterative learning update law based on the tracking error and the state. • The convergence condition is proved using fundamental mathematical properties • Two ILC schemes are presented, and a small comparison is given. The control of the MIMO system has become increasingly famous. However, most of the literature considers the linear system. This paper considers a non-linear MIMO wave equation. The control method proposed in this paper is the ILC controller with initial conditions unfixed. The chosen schemes in this paper are the PD-type ILC and the D-type ILC. Moreover, we give sufficient conditions to guarantee the methods' convergence. Finally, we present a simulation result on a specific numerical example to prove the effectiveness of the proposed control law with a comparison between both schemes. [ABSTRACT FROM AUTHOR]

An auxiliary filtering system approach is adopted in this paper to treat the interval observer design for linear systems with state and output disturbances. By augmenting the filtering system along with the disturbances boundaries, interval observer is built under the unknown input observer framework. Relying on the Lyapunov stability method and H ∞ technique, the existence of the interval observer is formulated into strict linear matrix inequalities instead of the combination of linear programming and linear matrix inequalities. Compared with the existing result, the proposed method could render tighter state intervals from simulation studies. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed state estimation problem for a linear time-invariant system characterized by fading measurements and random link failures. We assume that the fading effect of the measurements occurs slowly. Additionally, communication failures between sensors can affect the state estimation performance. To this end, we propose a Kalman filtering algorithm composed of a structural data fusion stage and a signal date fusion stage. The number of communications can be decreased by executing signal data fusion when a global estimate is required. Then, we investigate the stability conditions for the proposed distributed approach. Furthermore, we analyze the mismatch between the estimation generated by the proposed distributed algorithm and that obtained by the centralized Kalman filter. Lastly, numerical results verify the feasibility of the proposed distributed method. [ABSTRACT FROM AUTHOR]

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws. [ABSTRACT FROM AUTHOR]

This paper addresses a robust tube based model predictive control (RTBMPC) strategy for tracking problem of piecewise affine (PWA) linear systems. The core idea of the RTBMPC strategy is to robustly control an uncertain system through its nominal system and an additional feedback term which rejects a bounded additive disturbance. In tracking problem, RTBMPC strategy should be capable to steer the uncertain system to a given setpoint fulfilling the constraints. But if the setpoint changes, the controller may not success due to the loss of feasibility of the optimization problem. This paper employs several novel features to deal with tracking problem. First, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function. Then, the feasibility region is enlarged for given setpoint without increasing the prediction horizon by changing the terminal constraint set at different steps of RTBMPC problem solving. Simulation examples, including two different case studies, are presented to illustrate the effectiveness of the proposed RTBMPC. [ABSTRACT FROM AUTHOR]

This paper proposes a robust switched model-based predictive controller design for discrete linear systems with state constraints, inputs, and disturbances limited in norm. Modeled via linear matrix inequalities, the online and offline designs of the proposed control aim at minimizing the upper bound of the quadratic performance index for a horizon of infinite prediction associated with the state estimator and the switching rule, seeking to guarantee the robust stability for closed-loop systems. To this end, three theorems are formulated. To demonstrate the effectiveness of the control strategy, a comparative analysis is performed between the performance of the proposed model and a benchmark method. From the results, it is possible to conclude that the proposed method is promising in the scope of control of linear systems subject to switching, being more efficient than the benchmark for the stabilization and control of both numerical examples. [ABSTRACT FROM AUTHOR]

• The cascade augmented L-K functional method is proposed, the interconnect information among delayed state vectors is further used. • It is found that the proposed cascade augmented L-K functional is also suitable for linear systems with single time-delay if the delay-partitioning method is employed. Which means the cascade augmented L-K functional is more general. This paper investigates stability of linear systems with multiple/single time-delays. Firstly, a three-level cascade augmented Lyapunov-Krasovskii (L-K) functional is introduced, in which interconnect information among delayed state vectors is fully taken into account. Based on a newly integral inequality and the cascade L-K functional, a novel stability criterion is derived for linear systems with multiple time-delays. Secondly, it is found that the proposed L-K functional is also suitable for linear systems with single time-delay if the delay-partitioning method is employed. This motivates us to obtain a less conservative stability condition for linear systems with single time-delay. Finally, Numerical examples are given to confirm the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust distributed model predictive control with a self-triggered mechanism is proposed for a family of discrete-time linear systems with additive disturbances, local and global constraints. To handle the additive disturbances, a tube method is applied to achieve the robust satisfaction of local constraints. Meanwhile, a sequential constraints tightening method is proposed to guarantee the satisfaction of global coupled constraints. The optimization problem is constructed as a consensus problem of an augmented Lagrange function and is solved through a modified distributed alternative direction multiplier method. Furthermore, a self-triggered mechanism is adopted to help reduce the computation burden and accelerate system stabilization by skipping insignificant iteration steps in parallel ways. By clarifying the upper bound on tolerable bounded disturbances, two sufficient conditions about recursive feasibility of optimization problem and input-to-state stability of the closed-loop system are given, respectively. Finally, performances of the proposed scheme are illustrated by simulation examples. [ABSTRACT FROM AUTHOR]

The Kaczmarz method is one of the most simple and computationally efficient iterative methods for solving large-scale linear algebraic system of equations A x = b , which at each iteration of it, only one row of coefficient matrix need to be known. The aim of this paper is to derive the matrix form of Kaczmarz method for finding the solution of Sylvester matrix equation. First, we present an iterative algorithm for finding the solution of the matrix equation A X = F by extending the Kaczmarz method and obtain the convergence of it for any initial matrix. Then, by applying the hierarchical approach, we obtain a new iterative algorithm for solving the Sylvester matrix equation A X + X B = C. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed algorithm and compare with some similar gradient-based methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with event-triggered secure consensus for a class of linear multi-agent systems (MASs) under denial-of-service (DoS) attacks. Different from some existing methods, a multi-sensor multi-rate (MSMR) sampling mechanism is introduced to sample system states of agents. A class of multi-rate observer is devised to deal with some problems involved, such as the asynchrony and the incompleteness of several state sub-vectors, caused by the MSMR sampling mechanism. By using the partially updated state information of each agent, a novel multi-rate event-triggered mechanism is proposed, in which the continuous monitoring of the combined measurement information is avoided. Then, an event-based distributed secure consensus control protocol is presented against DoS attacks for the MAS under a directed communication topology. By taking into account the information on the duration and frequency of the DoS attacks, a sufficient condition is established to design suitable control protocols such that consensus can be achieved. Finally, a numerical example is provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we propose an interval-based state estimator for continuous-time linear systems with discrete-time measurements using an event-triggered mechanism and an explicit reachability method. An output injection method combined with a state variables permutation procedure are applied to design the robust estimator. In addition, the convergence of the proposed set-membership state estimator and the existence of a lower bound on the inter-event times are shown. Throughout a numerical example, the performance of this estimator are illustrated and compared to related works. [ABSTRACT FROM AUTHOR]

This paper addresses the leader-following H ∞ output consensus problem of heterogeneous linear multi-agent systems (MASs) under directed graphs. Both state feedback and output feedback based event-triggered control (ETC) protocols are developed. First, to avoid continuous communication between neighboring agents, the open-loop estimation method is used in the proposed ETC protocols. Second, a unified time- and event-triggering mechanism with an explicit minimum inter-event time (MIET) is further developed based on the open-loop estimation method so that Zeno behavior can be excluded. It is shown that under the proposed ETC protocols, the controlled MAS can achieve H ∞ output consensus. Finally, two numerical examples are provided to verify effectiveness of the proposed ETC protocols. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach for set-membership state estimation of switched discrete-time linear systems subject to bounded disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed and a new criterion is proposed to reduce the size of the zonotope at each sample time. The zonotopic set-membership estimator design for switched systems is provided within the LMI framework. The extension of the proposed scheme to deal with unknown inputs is also presented. An application to vehicle lateral dynamics state estimation is provided. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods. [ABSTRACT FROM AUTHOR]

This paper investigates secure bipartite consensus tracking of linear multi-agent systems under denial-of-service(DoS) attacks by using event-triggered control mechanism with data sampling. Both bipartite leader-following and containment tracking consensus are considered in this paper. The event-triggered control protocol using sampled-data information is designed to save limited resources. The communication channels are interrupted by intermittent DoS attacks. Sufficient conditions on the sampling periods, attack frequency and attack duration are obtained to ensure secure bipartite tracking consensus of the multi-agent systems. Finally, simulation example is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

• The concept of FTS and FTCS is proposed for general time-delay linear system. • The concept of FTS and FTCS is proposed for linear time-varying time-delay system. • Discussed the Lyapunov-Razumikhin condition for the above system. • Numerical simulations are illustrated. The primary goal of this paper is to examine the finite-time stability and finite-time contractive stability of the linear systems in fractional domain with time-varying delays. We develop some sufficient criteria for finite-time contractive stability and finite-time stability utilizing fractional-order Lyapunov-Razumikhin technique. To validate the proposed conditions, two different types of dynamical systems are taken into account, one is general time-delay fractional-order system and another one is fractional-order linear time-varying time-delay system, furthermore the efficacy of the stability conditions is demonstrated numerically. [ABSTRACT FROM AUTHOR]

This paper delves into the intricacies of addressing the fixed-time rotating encirclement problem encountered in linear multi-agent systems (FTREMAS). Our research culminates in the development of an encirclement protocol that remains unaffected by initial conditions of follower agents at the encirclement's settling time. Furthermore, we present a rotation method for follower agents which is more practical when compared to previous endeavors. Notably, as the targets themselves are in motion, we employ two distributed estimators to accurately estimate their positions and maintain distances during the encirclement. To ascertain system stability, we employ the Lyapunov technique for analysis. Finally, a simulation is conducted to demonstrate the effectiveness and performance of proposed methodology. • An encirclement protocol is presented for follower agents to encircle moving targets. • Fixed-time stability of protocol is analyzed to assure the independence of convergence rate. • Realistic rotating encirclement of follower agents around targets is considered. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of applying hybrid control to overcome overshoot performance limitations of linear time-invariant (LTI) systems, and puts forward a systematic method for the joint design of a hybrid controller. By modeling the whole closed-loop system in the framework of a hybrid system, an input-to-state stable (ISS) criterion for the system is established, and on the basis of this, conditions for non-overshooting step responses are obtained. In the proposed hybrid controller, apart from its input and output information, state information of the LTI plant and a basic LTI controller is used to design flow and jump sets. The advantage is that when the trigger matrix of flow and jump sets is unknown, it can be designed conveniently. Based on the conditions, the hybrid controller synthesis is formulated in linear matrix inequalities and the algorithm of solving controller matrices and the triggering matrix is given. In addition, the design method of the hybrid controller with a certain triggering matrix is derived. The effectiveness and reliability of the obtained results are demonstrated through a numerical example. [ABSTRACT FROM AUTHOR]

This paper proposes a robust digital sliding mode control design for multi-input linear systems that provides the closed-loop system dynamics of an arbitrary order having a specified feasible spectrum of poles. By appropriate selection of auxiliary outputs according to the controllability indices of the system, the system is decoupled into a set of subsystems. The number of these subsystems is equal to the number of control inputs. The desired dynamic of the considered system is achieved using discrete-time higher order sliding mode, where the discrete-time sliding mode of appropriate order is realized in each subsystem. The robustness is based on the fact that the previous values of the matched disturbances are directly reflected in the present value of the switching variables and it will be enhanced by using an estimator/compensator based on integral of sliding function. This control structure looks like discrete-time super-twisting control. Effectiveness of the proposed control is analyzed and its impact on the control system performances is derived. The proposed control approach is illustrated by simulation examples. [ABSTRACT FROM AUTHOR]