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This article presents an innovative technique for the black-box modeling of the conductive emissions of switching circuits from external observations. The proposed methodology relies on the robust and elegant theory of periodically switched linear systems, providing the user with a tool for the generation of frequency-domain augmented linear time-invariant equivalents. The obtained models offer both a remarkable accuracy for different supply conditions and a deep understanding of the inherent switching mechanisms of this class of devices. The proposed framework also enables the derivation of a simplified enhanced Norton representation which outperforms the classical state-of-the-art models based on linear time-invariant approximations. Model parameters are computed via a blind procedure based only on two measurements. The feasibility and strength of the proposed approach are demonstrated on a dc–dc boost power converter and on a dc electrical motor via the prediction of their conducted disturbances. [ABSTRACT FROM AUTHOR]

This paper studies the group consensus problem of second-order multi-agent systems (MASs) with switching communication topology. Unlike most existing papers concerning the consensus issue of MASs under arbitrary switching topology or Markovian switching topology, our paper tries to design a switching signal such that MAS can achieve group consensus under a designed switching signal set. First, using a state transformation method, the group consensus problem of MASs can be equivalently transformed into the asymptotical stability of a corresponding switched system. Then, two sufficient criteria are established by using Lyapunov function method and average dwell time (ADT) approach, where the minimum ADT τ a is given clearly. Finally, simulation examples are given to show the effectiveness of our theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper presents a unified approach to formulating stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation is generalized to the case of matrix-valued functions. Using this generalized concept, a result extending existing stability conditions for slowly time-varying linear systems is derived. As special cases of this result, two sets of stability conditions are derived for switched linear systems, which match known results in the literature. A numerical example is included to further illustrate the application of the main result. [ABSTRACT FROM AUTHOR]

The study is concerned with the filtering problem of discrete time positive switched delay systems under an improved delay-dependent persistent dwell time (PDT) switching, which includes delay-independent PDT switching as a special case. Under delay-dependent PDT switching, a pair of state bounding positive filters is designed such that the output of positive switched delay systems can be estimated at all times, and the effect of delay on PDT switching and the l1 performance is also discussed. Finally, a numerical example is presented to demonstrate the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

This paper investigates the bumpless transfer problem of switched linear systems with sensor faults. The framework of the switched control systems includes two kinds of controllers, one is for normal use and the other is for fault-tolerant control when sensor faults have occurred. Considering that the information of the sensor faults is unknown to the controller, an observer is designed for the fault-tolerant controller. Moreover, in view of the issue that the output difference between the online and offline controllers may induce undesired oscillations in control input at the switching instant, a bumpless transfer compensator is presented based on sliding mode control. Due to the reasonably designed compensator, the difference can be minimized to a small value to guarantee smooth transitions of the control input when sensor faults have occurred. Finally, numerical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Mode observability of switched systems requires observability of each individual mode. We consider other concepts of observability that do not have this requirement: Switching time observability and switch observability. The latter notion is based on the assumption that at least one switch occurs. These concepts are analyzed and characterized both for homogeneous and inhomogeneous systems. [ABSTRACT FROM AUTHOR]

In this paper, a switched control architecture for constrained control systems is presented. The strategy is based on command governor ideas that are here specialized to 'optimally' schedule switching events on the plant dynamics for improving control performance at the expense of low computational burdens. The significance of the method mainly lies in its capability to avoid constraints violation and loss of stability regardless of any configuration change occurrence in the plant/constraint structure. To this end, the concept of model transition dwell time is used within the proposed control framework to formally define the minimum time necessary to enable a switching event under guaranteed conditions on the overall stability and constraint fulfilment. Simulation results on a simple linear system and on a Cessna 182 aircraft model show the effectiveness of the proposed strategy. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and stabilization for switched systems with mode-dependent average dwell time (MDADT) switching are revisited and discussed in both continuous-time and discrete-time contexts. By introducing a class of quasi-alternative switching signals, some improved stability conditions of switched systems with MDADT are obtained. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. Then, based on the stability result, stabilization conditions for switched linear systems comprising uncontrollable subsystems are presented to guarantee the underlying system to be exponentially stable. The criteria obtained for the considered switched linear systems are all provided in terms of a set of linear matrix inequalities. To illustrate the advantages of our established results, a numerical example is finally given. [ABSTRACT FROM AUTHOR]

An effective way to deal with uncertainties in control of uncertain switched linear systems is so-called guaranteed cost control (GCC). Existing works on the GCC of these systems only provide asymptotical stability analysis. This paper focuses on the GCC to provide exponential stability in these systems. To this end, we design a new switching strategy and a state-feedback controller to exponentially stabilize the GCC of continuous-time switched linear systems with norm-bounded uncertainties. First, a new switching strategy is designed based on the common Lyapunov function technique and min-projection strategy. Second, a sufficient condition on the existence of proposed switching strategy is presented in the form of linear matrix inequalities. It is proved that the system to be exponentially stable under applying this switching strategy and guaranteed cost value and convergence rate of states are calculated. Finally, some numerical examples and comparisons are performed. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of model reduction for a class of switched linear parameter varying (LPV) systems with persistent dwell-time (PDT) switching property. The PDT switching generalizes the dwell-time and average dwell-time switching that are commonly concerned in the existing literature. To reduce the original high-order model with less conservatism, the constructed reduced-order model is both parameterized and semi-time-varying such that the model error system is uniformly stable over the PDT switching and guarantees an error performance in H ∞ sense. A numerical example is used to verify the validity and advantage of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with theH∞filtering problem for a class of continuous-time linear switched systems with the asynchronous behaviours, where ‘asynchronous’ means that the switching of the filters to be designed has a lag to the switching of the system modes. By using the Lyapunov-like functions and the average dwell time technique, a sufficient condition is obtained to guarantee the asymptotic stability with a weightedH∞performance index for the filtering error system. Moreover, the results are formulated in the form of linear matrix inequalities that are numerical feasible. As a result, the filter design problem is solved. Finally, an illustrative numerical example is presented to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

The output regulation problem of switched linear multi-agent systems with stabilisable and unstabilisable subsystems is investigated in this paper. A sufficient condition for the solvability of the problem is given. Owing to the characteristics of switched multi-agent systems, even if each agent has its own dwell time, the multi-agent systems, if viewed as an overall switched system, may not have a dwell time. To overcome this difficulty, we present a new approach, called an agent-dependent average dwell time method. Due to the limited information exchange between agents, a distributed dynamic observer network for agents is provided. Further, a distributed dynamic controller based on observer is designed. Finally, simulation results show the effectiveness of the proposed solutions. [ABSTRACT FROM PUBLISHER]

This paper investigates the finite-time filter design problem for a class of switched linear systems with parameter uncertainties and impulsive effects. The sensor failures with output-measurement errors and mode-detection delays are taken into account. A filter mode-dependent Lyapunov-like function construction approach is developed which can effectively reduce the filter design difficulty induced by the mode-detection delays. Sufficient conditions on finite-time boundedness and finite-time H ∞ performance are first derived for the augmented switched error systems, upon which the mode-dependent finite-time H ∞ filter is designed. Performance of the potential of the developed filter is illustrated by a numerical example and an application to PWM (Pulse-Width-Modulation)-driven boost converter. [ABSTRACT FROM AUTHOR]

In the theory of linear switching systems with discrete time, as in other areas of mathematics, the problem of studying the growth rate of the norms of all possible matrix products A σ n ⋯ A σ 0 with factors from a set of matrices A arises. So far, only for a relatively small number of classes of matrices A has it been possible to accurately describe the sequences of matrices that guarantee the maximum rate of increase of the corresponding norms. Moreover, in almost all cases studied theoretically, the index sequences { σ n } of matrices maximizing the norms of the corresponding matrix products have been shown to be periodic or so-called Sturmian, which entails a whole set of "good" properties of the sequences { A σ n } , in particular the existence of a limiting frequency of occurrence of each matrix factor A i ∈ A in them. In the paper it is shown that this is not always the case: a class of matrices is defined consisting of two 2 × 2 matrices, similar to rotations in the plane, in which the sequence { A σ n } maximizing the growth rate of the norms ‖ A σ n ⋯ A σ 0 ‖ is not Sturmian. All considerations are based on numerical modeling and cannot be considered mathematically rigorous in this part; rather, they should be interpreted as a set of questions for further comprehensive theoretical analysis. [ABSTRACT FROM AUTHOR]

Discrete-time dual switching linear systems are piecewise linear systems subject to both stochastic and deterministic commutations. Stochastic jumps, well-suited to account for unpredictable events like faults or abrupt changes in the parameters, are modeled by means of a Markov chain. The deterministic switches are dictated by a scheduling signal, used as a control variable in order to achieve stochastic stability and guaranteed input/output performance. We derive sufficient conditions for the existence of a state-feedback switching law attaining these goals. Further, the more challenging co-design problem is addressed, namely the joint synthesis of a linear state-feedback controller and a stabilizing switching strategy ensuring a prescribed performance. The results are illustrated by means of a numerical example concerning a networked control system under occasional communication failures. [ABSTRACT FROM AUTHOR]

This paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti-windup compensator. The closed-loop system consisting of the plant, the controller and the anti-windup compensator is first equivalently formulated as a linear system with input deadzone. We then partition the input space into several regions. In one of these regions, all inputs saturate with the time-derivative of the saturated input being zero. In each of the remaining regions, there is a unique input that does not saturate. The time derivative of the deadzone function associated with the unsaturating input is zero. By utilizing these special properties of the inputs on an existing piecewise Lyapunov function of the augmented state vector containing the deadzone function of inputs, we design a separate anti-windup gain for each region of the input space. The switching from one anti-windup gain to another is activated when the input signals leave one region for another, which can be implemented online since only the measurement of the input signals is required. Simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive control for a class of continuous-time switched linear systems is studied using a state-dependent switching method. All subsystems of the switched system under study can be unstable. First, an adaptive controller and a variable structure (VS) switching law with sliding sector are proposed, and some conditions are established in terms of linear matrix inequalities to guarantee the underlying system to be asymptotically stable. Then the problem of robust $$H_{\infty }$$ control for the systems under study is also solved by designing a proposed adaptive controller and a VS switching law. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Consensus problem for high-order multi-agent systems is considered under deterministic and Markovian switching topologies. Only relative output information of agents is assumed to be available through the networks. First, a necessary and sufficient condition for achieving a consensus under a fixed communication network is presented. Based on this result and the stability of switched systems, a high-order multi-agent system with the proposed low-gain controller is shown to reach a consensus under deterministic switching network if the total time when the network is disconnected is, in some senses, smaller than the total time of the network being connected. Furthermore, the conditions sufficient for a high-order multi-agent system to reach an almost sure and mean-square consensus, under Markovian switching networks, are presented. Finally, illustrative examples are given to demonstrate the results. [ABSTRACT FROM AUTHOR]

In this paper, the method to design the reduced-order switching function for an uncertain linear system in special coordinate basis (SCB) form is proposed. The sliding mode control with this method guarantees the asymptotic stability of all the states of system in presence of matched disturbance. The proposed design method is applicable to the system with unstable internal dynamics as well. This method enables the option of designing the control law with reduced-order states that are involved in the design of switching function. Also, a high performance sliding mode step-tracking control for non-minimum phase systems using reduced-order nonlinear switching function is proposed. The method is also extended to multiple-input and multiple-output (MIMO) systems. An effectiveness of sliding mode control with reduced-order switching function is shown through numerical examples. [ABSTRACT FROM PUBLISHER]

Alternative conditions for establishing dwell-time stability properties of linear switched systems are considered. Unlike the hybrid conditions derived in Geromel and Colaneri (2006), the considered ones are affine in the system matrices, allowing then for the consideration of uncertain switched systems with time-varying uncertainties. The low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state-feedback control laws. The resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped-functionals previously considered in the literature. The sums of squares conditions are also proven to (1) approximate arbitrarily well the conditions of Geromel and Colaneri (2006); and (2) be invariant with respect to time-scaling, emphasizing that the complexity of the approach does not depend on the size of the dwell-time. Several comparative examples illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of weighted H∞ filtering for a class of switched linear systems with two additive time-varying delays, which represent a general class of switched time-delay systems with strong practical background. Combining average dwell time (ADT) technique with piecewise Lyapunov functionals, sufficient conditions are established to guarantee the exponential stability and weighted H∞ performance for the filtering error systems. The parameters of the designed switched filters are obtained by solving linear matrix inequalities (LMIs). A modification of Jensen integral inequality is exploited to derive results with less theoretical conservatism and computational complexity. Finally, two examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a saturation-based switching anti-windup design for the enlargement of the domain of attraction of a linear system subject to nested saturation. A nestedly saturated linear feedback is expressed as a linear combination of a set of auxiliary linear feedbacks, which form a convex hull where the nestedly saturated linear feedback resides. This set of auxiliary linear feedbacks is then partitioned into several subsets. The auxiliary linear feedbacks in each of these subsets form a convex sub-hull of the original convex hull. When the value of the nestedly saturated linear feedback falls into a convex sub-hull, it can be expressed as a linear combination of the subset of all the auxiliary feedbacks that form the convex sub-hull. A separate anti-windup gain is designed for each convex sub-hull by using a common quadratic Lyapunov function and is implemented when the value of the nestedly saturated linear feedback falls into this convex sub-hull. Simulation results indicate that such a saturation-based switching anti-windup design has the ability to significantly enlarge the domain of attraction of the closed-loop system. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov–Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov–Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov–Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H∞ performance costs are bounded above by a constant value. These results are illustrated with some numerical examples. [ABSTRACT FROM AUTHOR]

A distributed dynamic output feedback control is designed by Scardovi and Sepulchre for the synchronisation of a network of identical linear systems, known as agents in literature. The design is based on some mild conditions allowing switching topology. However, it assumes that there is no time delay in signal transfer between the neighbouring agents. In this study, the authors extend their work to include known time delay in communications. Furthermore, the authors' design has some special features: (i) the delay can be arbitrary and only need to be uniformly bounded by a constant; (ii) the conditions that time delay should be the same and sufficiently small in some literature are not required here; and (iii) no local buffer is required to store past data because of time-delay effect. [ABSTRACT FROM AUTHOR]

This paper presents recent developments in the study of non-autonomous switching linear systems. For such systems, we address the issue of how to systematically design linear controllers allowing the active process mode to be observable from closed-loop data. The results are stated formally by introducing the notion of discerning controllers . Both existence and genericity problems are discussed. It is finally shown how a given family of discerning controllers can be implemented as a single hybrid system which preserves the discerning capability of the original controllers. Examples are discussed to substantiate the analysis. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with Markovian switching. The uncertain stochastic system with Markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix. New criteria for testing the robust stability of such systems are established in terms of bi-linear matrix inequalities (BLMIs), and sufficient conditions are proposed for the design of robust state-feedback controllers. A numerical example is given to illustrate the effectiveness of our results. [Copyright &y& Elsevier]

This paper deals with the problem of state feedback stabilization with finite-time stochastic stability for a class of discrete-time switched stochastic linear systems under asynchronous switching. The attention is focused on designing the feedback controller that guarantees the finite-time stochastic stability of the dynamic system. The finite-time stochastic stability definition of discrete-time switched stochastic systems is introduced. The asynchronous switching idea originates from the fact that switching instants of the controllers lag behind or exceed those of subsystems. On the basis of the average dwell time method and multiple Lyapunov functions approach, a finite-time stochastic stability condition is established. Then, an asynchronously switched controller is designed and the corresponding switching law is derived to guarantee the considered system be finite-time stochastically stable. Two numerical examples are provided to show the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

The sign stability concept in ecological systems is introduced into the analysis and synthesis of switched linear system to explore new control design technique. The necessary and sufficient condition for sign stability of a switched linear system under arbitrary switching is achieved via the notion of complete isogenous sign stable set (CISSS). A new approach for the stabilization of switched system is presented. Although the controllers are devised for each subsystem, respectively, the switched system is sign stabilized by the constitution of CISSS. The provided method has natural robustness and more design freedoms than the familiar Lyapunov function method, which bears relative conservativeness as the requirement of solving LMIs. The presented technique is validated by an example of flight control within a large-scale flight envelop. Simulation results indicate that the proposed method can stabilize the flight attitude under large variations of system parameters and external perturbations. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of fault detection and isolation (FDI) for discrete-time switched linear systems based on the average dwell-time method. The proposed FDI framework consists of a bank of FDI filters, which are divided intoNgroups forNsubsystems. The FDI filters belonging to one group correspond to the faults for a subsystem, and generate a residual signal to guarantee the fault sensitivity performance for the subsystem, the fault attenuation performance for other subsystems and the disturbance attenuation performance for all subsystems. Different form employing the weighting matrices to restrict the frequency ranges of faults for each subsystem, the finite-frequencyH−performance for switched systems is first defined. Sufficient conditions are established by linear matrix inequalities (LMIs), and the filter gains are characterised in terms of the solution of a convex optimisation problem. Two examples are used to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on the passivity analysis and feedback passification for switched discrete-time linear systems using multiple storage functions under a certain switching law. Controllers and switching laws are designed based on complete and partial state measurements, respectively. Conditions for strict passivity of a switched discrete-time system are obtained without the requirement of strict passivity of subsystems. In the case of partial state measurements, dynamic output feedback controllers for subsystems are designed, and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed-loop switched system. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical results. [Copyright &y& Elsevier]

Abstract: A new method to find an upper bound on dwell time and average dwell time for switched linear systems is proposed. The method is based on computing the maximum cycle ratio and the maximum cycle mean of the directed graph that governs switchings. For planar switched systems, an upper bound for dwell time and average dwell time can be estimated by considering only the cycles of length two. [Copyright &y& Elsevier]

Abstract: The paper presents realization theory of discrete-time linear switched systems. We present necessary and sufficient conditions for an input–output map to admit a discrete-time linear switched system realization. In addition, we present a characterization of minimality of discrete-time linear switched systems in terms of reachability and observability. Further, we prove that minimal realizations are unique up to isomorphism. We also discuss algorithms for converting a linear switched system to a minimal one and for constructing a state-space representation from input–output data. The paper uses the theory of rational formal power series in non-commutative variables. [Copyright &y& Elsevier]

This paper is concerned with the design of positive observers for switched positive linear systems with time-varying delays. Attention is focused on designing the positive observers such that the error switched systems are exponentially stable. Based on the average dwell time approach, sufficient conditions, which ensure the estimated error exponentially converges to zero, are formulated in a set of linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies both continuous and discrete time consensus problems for multi-agent systems with linear time-invariant agent dynamics over randomly switching topologies. The switching is governed by a time-homogeneous Markov process, whose state corresponds to a possible interaction topology among agents. Necessary and sufficient conditions are derived for achieving consensus under a common control protocol, respectively. It is shown that the effect of switching topologies on consensus is determined by the union of topologies associated with the positive recurrent states of the Markov process. Moreover, the effect of random link failures on discrete time consensus is investigated. The implications and relationships with the existing results are discussed. Finally, the theoretical results are validated via simulations. [Copyright &y& Elsevier]

This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference (Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20(12), 4105–4109 (2010)), a nonlinear feedback gain is needed to generate chaotic dynamics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the controller is constructed by Russell’s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller. [ABSTRACT FROM AUTHOR]

The leader-following consensus of high-order multi-agent linear systems with bounded transmission channels is considered. Agents modelled as LTI dynamics exchange information according to a network which can be described as a graph with agents as its vertices and information transmission channels as its edges. The transmission channels are bounded. The objective is leader-following in the sense that the state of all agents should converge to that of the leader vehicle. Detailed analysis of the leader-following consensus under bounded transmission channels is investigated for both fixed and switching network topologies. [ABSTRACT FROM PUBLISHER]

Abstract: This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics for both the cases without and with a leader whose control input might be nonzero and time varying. For the case without a leader, based on the relative output information of neighboring agents, two types of distributed adaptive dynamic consensus protocols are proposed, namely, the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication graph and the node-based adaptive protocol which uses a time-varying coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for all undirected connected communication graphs. It is shown that the edge-based adaptive consensus protocol is applicable to arbitrary switching connected graphs. For the case where there exists a leader whose control input is possibly nonzero and bounded, a distributed continuous adaptive protocol is designed to guarantee the ultimate boundedness of the consensus error with respect to any communication graph which contains a directed spanning tree with the leader as the root and whose subgraph associated with the followers is undirected, requiring neither global information of the communication graph nor the upper bound of the leader’s control input. A distributed discontinuous protocol is also discussed as a special case. Simulation examples are finally given to illustrate the theoretical results. [Copyright &y& Elsevier]