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In this manuscript, it is investigated that the stability property of a discrete-time switched system consisting of all unstable subsystems. Under a switching signal with certain conditions, the sufficient constraints for asymptotic stability of a discrete-time switched system composed of all unstable subsystems are obtained via Lyapunov functions and the defined divergence time. Furthermore, based on this result, linear matrix inequalities are obtained for asymptotic stability of a linear discrete-time switched system composed of all unstable subsystems. The efficiency of the acquired theorems is exhibited by three numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of asymptotic stability of a kind of nonlinear perturbed neutral differential system with variable delay is discussed. The Lyapunov-Krasovskiˇı functional constructed, is used to obtain conditions for asymptotic stability of the nonlinear perturbed neutral differential system in terms of linear matrix inequality (LMI). The two new results (delay-independent and delay-dependent criteria) include and extend the existing results in the literature. Finally, an example of delay-dependent criteria is supplied and the simulation result is shown to justify the effectiveness and reliability of the used techniques. [ABSTRACT FROM AUTHOR]

To address the nonlinear stabilization problem and improve the tracking control feature of ball on plate system (BPS), this paper puts forward a novel Takagi Sugeno (TS) fuzzy control augmented with the current cycle feedback iterative learning control (CCF-ILC) scheme. According to Bode's sensitivity integral, the performance of linear controllers is always a trade-off between reference tracking and robustness. Hence, to deal with the so-called 'waterbed' effect, this work exploits the capability of TS fuzzy to handle the nonlinear dynamics and synthesizes a learning control scheme based on current iteration error to capitalize the information rich error signal for enhancing the robustness and trajectory tracking features. The global asymptotic stability of the proposed TS fuzzy augmented ILC scheme is proved using the Lyapunov function and linear matrix inequalities (LMIs). Moreover, the monotonic convergence of ILC is presented based on the singular value condition. For identifying the rolling mass from the video stream, a background subtraction algorithm based on thresholding technique is implemented. Finally, the robustness and tracking features of the proposed scheme are evaluated on a two degrees of freedom (DoF) laboratory scale BPS system through hardware in loop (HIL) testing for three realistic test cases. The tracking performance quantified using the root mean square error (RMSE) and power spectral density plot corroborates that the proposed scheme can offer better setpoint tracking and robustness feature compared to state-of-the-art fuzzy and ILC control techniques implemented on BPS. [ABSTRACT FROM AUTHOR]

Attitude control of a satellite with three flexible elements is considered. Control torque is developed by a set of reaction wheels, which are installed on the central hub of the satellite. The flexible elements are large, so the control torque constraints must be taken into account. In the paper, a control algorithm based on a linear-quadratic regulator is studied. The asymptotic stability of this control is shown. The choice of the control parameters is based on the closed form solution of the corresponding algebraic Riccati equation, which is supplemented by the linear matrix inequality. To increase the convergence rate, particle swarm optimization is used to tune the control parameters. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic stability of fractional-order neural networks (FONNs) with time delay utilizing a sampled-data controller. Firstly, a novel class of Lyapunov–Krasovskii functions (LKFs) is established, in which time delay and fractional-order information are fully taken into account. Secondly, by combining with the fractional-order Leibniz–Newton formula, LKFs, and other analysis techniques, some less conservative stability criteria that depend on time delay and fractional-order information are given in terms of linear matrix inequalities (LMIs). In the meantime, the sampled-data controller gain is developed under a larger sampling interval. Last, the proposed criteria are shown to be valid and less conservative than the existing ones using three numerical examples. [ABSTRACT FROM AUTHOR]

This article discusses the problems of admissibility for uncertain T–S fuzzy singular systems with time-varying delay. Firstly, a model which transforms the original system into two interconnected systems by two-term approximation of the delayed state based on small gain theorem is proposed. Then, the generalized integral inequality method is used to derive the admissibility conditions for uncertain T–S fuzzy singular systems. Moreover, to account for the generalized integral inequality, new augmented Lyapunov–Krasovskii functional is constructed with some new terms. Consequently, the developed criteria are given in terms of linear matrix inequalities "LMIs," which provide less conservative results than some recent existing ones in the literature. Finally, numerical examples are given to demonstrate the applicability and the effectiveness of the developed method in this article. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of asymptotic stability with Hankel norm performance (HNP) of two-dimensional (2-D) digital filter characterised by Roesser model, where the 2-D system includes overflow nonlinearities and external interference or excitation of finite duration. The underlying nonlinearities cover the usual types of overflow arithmetic utilised in practice such as saturation, two's complement, zeroing and triangular. To solve this problem, new sufficient criterion is proposed by employing quadratic 2-D Lyapunov function. The proposed criterion guarantees that the addressed system has 2-D HNP bound. This criterion can examine the unwanted memory effect (ME) reduction of 2-D interfered digital filters for past excitations. In the absence of external inputs, the asymptotic convergence of 2-D digital filters is established under the proposed criterion. The developed HNP criterion is in linear matrix inequality framework and, therefore, computationally tractable. In addition, the optimisation problem is formulated to obtain the minimum HNP of the 2-D interfered digital filter. To illustrate the effectiveness of the proposed criterion, a numerical example is provided. The criteria addressed in current paper can give a whole analysis framework for the unwanted MEs of filters. [ABSTRACT FROM AUTHOR]

In this digital era, the basis of every smart instrument is discrete signal models e.g. in Networked control systems, Cyber physical systems etc. It has been shown that time-delays are unavoidable during the digital implementation of an engineering system. Therefore, the stabilization of discrete time delayed systems is gaining the high importance [1–10]. Although a lot of literature is found on the stabilization of time delayed systems for a long time using the construction of proper non-negative Lyapunov functional. Recalling some existing results on this issue, the LMI-based stability conditions are obtained by its forward difference negative-definite in direction to claim the less conservative results [15–25]. In order to seek less conservative stability criteria, this paper introduces an anti-windup scheme appended with Wirtinger inequality, reciprocal convex approach and delay partitioning of a discrete-time delayed systems by using Lyapunov Krasovskii functional. To accomplish this task, delay partitioning technique may be utilized to develop improved stability conditions for the considered system. The Wirtinger-based inequality and reciprocal convex approach has been employed to derive less conservative results. On employing the delay partitioning, a novel linear matrix inequality-based criterion is proposed to stabilize such systems. The considered Lyapunov-Krasovskii functional includes the information of intermediate delay to acknowledge the delay information implicitly that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. The estimation of the attraction basin is to ensure that the state remains inside the level set of a certain Lyapunov function. Numerical simulation verifies that the presented method reduces conservatism than the existing results. [ABSTRACT FROM AUTHOR]

This paper addresses the design of a dynamic output feedback-based anti-windup compensator to mitigate the windup phenomenon for a discrete time-varying delayed system with input saturation to establish the asymptotic stability. Linear matrix inequalities–based stability conditions are derived locally and globally. The controller for the closed-loop system is designed to reduce the effect of external bounded disturbances by utilizing the linear matrix inequality approach. The novel triple Lyapunov–Krasovskii functional along with reciprocal convex inequality is used to solve the expressions contained in the forward difference of the functional and to maximize the basin of attraction. Finally, industrial examples are simulated to prove the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

This paper investigates the stability for a class of distributed-order nonlinear systems via event-triggered control method. First of all, an inequality of the solution is established for distributed-order nonlinear inequality systems by employing Laplace transform. And then, by designing an appropriate state feedback controller and event-triggered strategy, and using Lyapunov stability theory and matrix inequality technique, a sufficient condition to ensure the asymptotic stability of the considered distributed-order nonlinear systems is obtained in the form of linear matrix inequality. Moreover, a criterion to exclude Zeno behaviour in event-triggered strategy is provided. Finally, the feasibility and effectiveness of the proposed method are verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an infinite set of lifting functions. A finite-dimensional approximation of the Koopman operator can be identified from data by choosing a finite subset of lifting functions and solving a regression problem in the lifted space. Existing methods are designed to identify open-loop systems. However, it is impractical or impossible to run experiments on some systems, such as unstable systems, in an open-loop fashion. The proposed method leverages the linearity of the Koopman operator, along with knowledge of the controller and the structure of the closed-loop (CL) system, to simultaneously identify the CL and plant systems. The advantages of the proposed CL Koopman operator approximation method are demonstrated in simulation using a Duffing oscillator and experimentally using a rotary inverted pendulum system. An open-source software implementation of the proposed method is publicly available, along with the experimental dataset generated for this paper.

In this paper, the problem of state estimation is investigated for a class of discrete-time complex-valued neural networks (CVNNs) with both leakage delay and discrete time-varying delays. The signal transmission from output sensors to state estimator is implemented via a shared wireless network with limited communication resources. For the aim of reducing the consumption of limited communication resources, the transmission strategy based on dynamic event-triggering is introduced to determine when the updating of the output measurement should be carried out. By taking use of some properties of Hermitian matrix and constructing an appropriate Lyapunov–Krasovskii functional, a sufficient criterion is derived for ensuring the asymptotical stability of the estimation error system without separating the CVNN to its real-part system and imagination one is derived, which is quite different from those approach used in exiting literature. The gain matrix for estimator is designed by resorting to a set of feasible solutions of linear matrix inequalities (LMIs) with complex-valued variables. A numerical example and its simulation results are given to illustrate the validity of the theoretical result. [ABSTRACT FROM AUTHOR]

This article concentrates on the asymptotic stabilization problem of switched affine systems (SASs) with unmeasurable states and time delay by constructing a novel dynamic event‐triggered mechanism (ETM). Given the limited network transmission and the difficulties caused by affine terms in excluding the triggering Zeno behavior, we propose a novel dynamic ETM. It has been shown that the dynamic ETM not only has fewer data transfers than the existing ETM but also avoids Zeno behavior while maintaining asymptotic stability. Then, by constructing a set of dynamic output feedback switched affine controllers and switching laws, delicately incorporating Lyapunov–Krasovskii functionals, an asymptotic stabilization criterion is derived for the closed‐loop SASs. The design methods of the controllers and switching laws are skillfully implemented by solving a set of linear matrix inequalities. Finally, an application example of the flyback DC–DC converter is offered to verify the proposed algorithm. [ABSTRACT FROM AUTHOR]

The lack of a conventional Lyapunov theory for fractional-order (FO) systems makes it difficult to study the dynamics of fractional-order neural networks (FONNs). Instead, the existing literature derives necessary conditions for various dynamic properties of FONNs using Halanay-type lemmas. However, when these lemmas are used, the results are frequently more conservative than those produced for integer-order neural networks (NNs). In order to provide sufficient criteria that are less conservative than those found in other research, a novel application of the Halanay-type lemma is made within this study. Thus, for extremely general FONNs containing neutral-type, time-varying, and distributed delays, sufficient conditions presented by way of linear matrix inequalities (LMIs) and algebraic inequalities are achieved. For the FO scenario, a model this broad and including so many different kinds of delays is developed for the first time. Additionally, a novel form of Lyapunov-like function is built, which results in less stringent algebraic inequalities. One of the first times in the setting of FONNs, the free-weighting matrix method is also used to further lower the conservativeness of the obtained conditions. Based on different Lyapunov-type functions, three theorems are developed regarding the asymptotic stability of the proposed networks. Three numerical simulations are used to demonstrate the theoretical developments. [ABSTRACT FROM AUTHOR]

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article investigates the admissibility analysis for Takagi–Sugeno fuzzy singular systems (T–S FSSs) with time-varying delays. First, according to the decomposed state vectors, a state decomposition Lyapunov–Krasovskii functional (LKF) is constructed, which possesses fewer decision variables. And, the LKF is augmented by considering more features of the second-order Bessel–Legendre inequality (BLI). Then, the second-order BLI and the generalized reciprocally convex matrix inequality are employed to dispose the derivative of the LKF, where the $d^{2}(t)$ -dependent term exists. Meanwhile, by setting an adjustable parameter, the $d^{2}(t)$ -dependent term of the condition is handled by a relaxed quadratic function negative-determination condition. As a result, a less conservative admissibility criterion for T–S FSSs is obtained. And, the relationship between the conservatism and the numerical burden is better considered. Finally, a numerical example is given to demonstrate the reduced conservatism and computational complexity. [ABSTRACT FROM AUTHOR]

Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two methods for approximating the Koopman operator, are reformulated as convex optimization problems with linear matrix inequality constraints. Asymptotic stability constraints and system norm regularizers are then incorporated as methods to improve the numerical conditioning of the Koopman operator. Specifically, the H∞ norm is used to penalize the input–output gain of the Koopman system. Weighting functions are then applied to penalize the system gain at specific frequencies. These constraints and regularizers introduce bilinear matrix inequality constraints to the regression problem, which are handled by solving a sequence of convex optimization problems. Experimental results using data from an aircraft fatigue structural test rig and a soft robot arm highlight the advantages of the proposed regression methods. [ABSTRACT FROM AUTHOR]

This article proposes improved stability and stabilization criteria for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. First, a novel augmented fuzzy Lyapunov–Krasovskii functional (LKF) including the quadratic fuzzy Lyapunov matrix is constructed, which can provide much information of T–S fuzzy systems and help to achieve the lager allowable delay upper bounds. Then, improved delay-dependent stability and stabilization criteria are derived for the studied systems. Compared with the traditional methods, since the third-order Bessel–Legendre inequality and the extended reciprocally convex matrix inequality are well employed in the derivative of the constructed LKF to give tighter bounds of the single integral terms, the conservatism of derived criteria is further reduced. In addition, the quadratic fuzzy Lyapunov matrix introduced in LKF, which contains the quadratic membership functions, is also an important reason for obtaining less conservative results. Finally, numerical examples demonstrate that the proposed method is less conservative than some existing ones and the studied system can be well controlled by the designed controller. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic stability problem of neural networks with time-varying delays is investigated. First, a new sufficient and necessary condition on a general polynomial inequality was developed. Then, a novel augmented Lyapunov–Krasovskii functional (LKF) was constructed, which efficiently introduces some new terms related to the previous information of neuron activation function. Furthermore, based on the suitable LKF and the stated negative condition of the general polynomial, two criteria with less conservatism were derived in the form of linear matrix inequalities. Finally, two numerical examples were carried out to confirm the superiority of the proposed criteria, and a larger allowable upper bound of delays was achieved. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability analysis for the fuzzy-based sampled-data control (SDC) systems, which is based on a fractional parameter-based refined looped-Lyapunov functional (RLLF). To do this, with the help of the Takagi–Sugeno fuzzy method, a SDC can be designed. To derive sufficient criteria, a RLLF with information about the sampling period is proposed. In the RLLF, a fractional parameter is introduced and it has more information on the splitted sampling intervals and delayed states with a fractional parameter. The derived criteria guarantee the asymptotic stability of the proposed system with a $H_{\infty }$ attenuation level. To validate the derived conditions, a state-space model of nonlinear permanent magnet synchronous motor is proposed. Besides, comparison examples are conducted for analyzing the less conservatism of the merit of the proposed methods. Finally, the simulation outcomes are illustrated the superiority of the work. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear perturbed system of neutral delay integro-differential equations (NDIDEs). We prove two new theorems, Theorems 1 and 2, such that these theorems include sufficient conditions and are related to asymptotical stability of zero solution of the perturbed system of NDIDEs. The technique of the proofs depends upon the definitions of two new and more suitable Lyapunov-Krasovskiĭ functionals (LKFs). When we compared the results of this paper with those found in the literature, our results improve and extend some classical results, and contribute new contents to the topic of NDIDEs and to the profession. [ABSTRACT FROM AUTHOR]

The asymptotic stability of delayed reaction-diffusion neural networks with algebraic constraints, that is, singular delayed reaction-diffusion neural networks, is studied in this paper. In terms of Green's theorem, inequality technique and linear matrix inequalities (LMIs), two less conservative criterion for the asymptotic stability of singular delayed reaction-diffusion neural networks are given by endowing Lyapunov direct method and used to design an appropriate stabilizing feedback controllers. The results address both the effects of the delay and the algebraic constraints. In addition, these conditions have higher computational efficiency and can easily detect and stabilize the actual neural networks. Finally, the numerical simulations verify the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we investigate the parabolic partial differential equations (PDEs) systems with Neumann boundary conditions via the Takagi–Sugeno (T–S) fuzzy model. On the basis of the obtained T–S fuzzy PDE model, a novel fuzzy state controller which is associated with the boundary state of position and the mean value coefficient matrix derived through the mean value theorem of integral is designed to analyze the asymptotic stability of the parabolic PDE system. Without sampling the nonlinear parameter of the system, new stability conditions are deduced in the form of linear matrix inequalities (LMIs). Moreover, compared with the novel fuzzy state controller, more conservative conditions based on another fuzzy state controller are also provided. Finally, we explore the state-feedback controller into the Fisher equation as an application. Simulation results show that the proposed method is effective. [ABSTRACT FROM AUTHOR]

This letter presents a novel global asymptotic stability (GAS) criterion for fixed-point digital filters (DFs) employing saturation overflow arithmetic. The criterion is developed using an improved characterization of saturation nonlinearities (as prevailing in the DF under study) and Lyapunov theory. The criterion outperforms a series of existing criteria. [ABSTRACT FROM AUTHOR]

This article presents a new asymmetric Lyapunov–Krasovskii functional method on the stability and stabilization of Takagi–Sugeno fuzzy systems with time delay. For the reduction of conservativeness, combining the method with the membership-function-dependent approach, we propose a novel delay-dependent stability condition in the form of linear matrix inequalities. Based on the condition, we further obtain a novel condition of stabilization. At the end, we provide two numerical examples to verify the advantage of the stability and stabilization approaches, respectively. [ABSTRACT FROM AUTHOR]

This article addresses the problem of finite-time almost sure stability, where the system is with Markov jump parameters and delayed inputs. With using Gronwall’s inequality and strong law of large numbers for Markov chains, finite-time bounded criteria and finite-time stability criteria are derived by Lyapunov–Krasovskii functional method. Moreover, a finite-time stability criterion in form of linear matrix inequality is given to design the controller gain. The obtained results are applied to finite-time sampled-data control of a truck-trailer system and finite-time control of a Markov jump mass-spring model with delayed inputs. [ABSTRACT FROM AUTHOR]

Singularly perturbed systems have found widespread applications in practice. The existing results on singularly perturbed systems mainly focused on the Lyapunov asymptotic stability, which are unable to deal with the cases that the system states cannot exceed a given threshold during a fixed time interval. This article addresses the finite-time fuzzy control issue for discrete-time nonlinear singularly perturbed systems with input constraints. The aim is to guarantee the boundedness of the states of singularly perturbed systems during a finite-time interval. Based on the matrix inequality technique, some conditions are established to guarantee the finite-time boundedness of the fuzzy singularly perturbed systems, where the singularly perturbed parameter is independent so as to avoid the ill-conditioned problem caused by the small singularly perturbed parameter. The gains of the finite-time fuzzy controller can be obtained by solving some singularly perturbed parameter independent linear matrix inequalities. Finally, the proposed finite-time fuzzy controller design approach for nonlinear singularly perturbed systems is illustrated via the Van der Pol circuit. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of neural network with time-varying delay. A new Lyapunov–Krasovskii functional (LKF) is constructed with some non-integral delay-product functional terms. Some parameter matrices in the LKF are not required to be positive definite. The convex method and the non-convex method are proposed to deal with the square of the time-varying delay appearing in the derivative of the LKF, respectively. Two less conservative delay-dependent stability criteria in the form of linear matrix inequalities (LMIs) are established. Finally, two widely used numerical examples are given to illustrate the validity and superiority of the obtained stability criteria. [ABSTRACT FROM AUTHOR]

This article proposes a resilient reliable $H_{\infty }$ load frequency control (LFC) design for power system involving the external load disturbances, stochastic actuator failures, and randomly occurring gain fluctuations. In this regard, the separate random variables are introduced which characterize the actuator failures and gain fluctuations in an individual manner that satisfies the Bernoulli distribution. The resilient reliable proportional–integral (PI)-type LFC is proposed by utilizing the resilient control scheme and the reciprocal convex technique along with the Lyapunov–Krasovskii functional (LKF), which guarantees the mean-square asymptotic stability of power system via $H_{\infty } $ performance index. Finally, the simulations are given to ensure the less conservative results of the proposed method when compared to the existing results. [ABSTRACT FROM AUTHOR]

In this brief, the structural stability of continuous fractional-order (FO) two-dimensional (2D) Fornasini-Marchesini (FM) first model is investigated. Firstly, the bivariate polynomial-based stability condition is equivalently transformed to be in more tractable form. Then, based on generalized KYP lemma, the transformed conditions are further reduced into the feasibility problem of linear matrix inequalities (LMIs). The main contribution is to establish the LMI-based stability conditions for continuous FO 2D FM first model. The results can be applied in the cases with FO $\alpha _{i} \in (0,2)$ and be no conservative when the FO in the second dimension $\alpha _{2} \in [1,2$). Lastly, the example is provided to verify the efficiency. [ABSTRACT FROM AUTHOR]

In this article, a new approach is proposed for stability analysis and controller design of nonlinear discrete-time positive systems by means of the Takagi–Sugeno fuzzy model. The closed-loop stability and the positivity constraint are guaranteed by synthesizing a linear co-positive Lyapunov function and by applying the parallel distributed compensation controller. In contrast to the state-of-the-art approaches for ensuring the $\ell _{1}$ -stability of the positive system which are based on bilinear matrix inequalities, the proposed optimal robust control design under $\ell _{1}$ -induced performance is derived based on linear programming framework. It has been shown that the computational complexity of the proposed optimization problem can be effectively reduced. Finally, a numerical example and the Leslie population model are adopted to show the capabilities of the proposed method. [ABSTRACT FROM AUTHOR]

This article concerns the problem of stability analysis of nonlinear systems under the sampled-data control (SDC) with actuator faults. The addressed nonlinear systems can be expressed by a number of linear arrangements, based on the Takagi–Sugeno (T–S) fuzzy technique. The time-dependent SDC with actuator faults of the addressed nonlinear systems delineates based on the input model of Markovian variability. The time-scheduled Lyapunov functional and the looped-functional are taken together in the production of a Lyapunov functional candidate. Based on a free matrix-based integral inequality and the Lyapunov functional, some sufficient linear matrix inequality conditions are delivered to guarantee the mean-square asymptotic stability under $H_\infty$ performance of the considered sampled-data T–S fuzzy systems with actuator faults. Finally, we demonstrate the feasibility and strength of our proposed method through some examples. [ABSTRACT FROM AUTHOR]

This article interrogates the issue of global asymptotic stability and synchronization analysis of uncertain multi‐agent systems (MASs) with multiple time‐varying delays (discrete and distributed) and impulsive perturbations. In this problem, we prove the existence and uniqueness of the equilibrium point using Brouwer degree properties for the addressed MASs. By applying the approach of Lyapunov–Krasovskii function into the considered system, we achieve the global asymptotic stability and the synchronization criteria by designing the pining control strategy into the MAS. Finally, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported in this article. [ABSTRACT FROM AUTHOR]

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Purpose: This paper deals with the problem of input/output-to-state stability (IOSS) of direct-form digital filters, which simultaneously contain external disturbances and two's complement nonlinearity. The nonlinearity under consideration is confined to the sector [–1, 1], which contains saturation, zeroing, two's complement and triangular. Design/methodology/approach: The proposed condition is based on IOSS approach, which is capable of providing a framework for checking and analysing the stability of nonlinear system based on input as well as output information. Findings: A linear matrix inequality (LMI)-based new sufficient criterion for the IOSS of the suggested system is obtained. The obtained criterion is capable of detecting the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with zero external disturbances. In addition, state-norm estimator for the filter under consideration is constructed by adopting an exponential-decay IOSS criterion. Several examples are provided to illustrate the usefulness of the proposed criteria. Originality/value: The result of the paper is introduced for the first time, and it is suitable for stability analysis of interfered direct-form digital filter with two's complement overflow using IOSS approach. [ABSTRACT FROM AUTHOR]

DC microgrid (DCMG) clusters represent interconnections of multiple DCMGs to enable flexible power flow, and hence advantages of high resilience, economic dispatch, loss minimization, and optimal load response with microgrid-based distributed generations can fully be taken. However, small-scale DCMGs are known to be weak in nature due to low inertia and high grid impedance. Meanwhile, dynamic analyses of DCMG clusters have been plagued by their high order dynamic nonlinear system models since numerous state variables are involved. This article proposes large signal stability analysis of DCMG clusters based on Takagi-Sugeno multimodeling approach. With the proposed method, the large signal Lyapunov stability of the DCMG cluster is reduced to the computation of a series of linear matrix inequalities, which will significantly simplify the analysis. The influences of circuit parameters, power flows, and topological change on large signal stability of the DCMG cluster are revealed, and asymptotic stability regions of the network are estimated as well. In addition to simulation verification, a laboratory prototype of a ring topology DCMG cluster with three 48 V DCMGs interconnected is also built to validate the analysis by experimental results. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the input-to-state stability (ISS) problem for a class of nonlinear systems with exogenous disturbances, where the states of the system are not fully available. Based on the idea of event-triggered control (ETC) strategy, a novel event-triggered mechanism (ETM) is designed to reduce the burden of the communication and controller updating with guaranteed performance requirement. Correspondingly, an observer-based impulsive controller coupled with sample control is proposed such that the controlled system is ISS under the designed ETM. Moreover, the possible accumulations of triggered instants (i.e., Zeno behavior) in the proposed control strategy are excluded. The controller gains and ETM parameters are co-designed by solving linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This article study the asynchronous control problem for a class of discrete-time Markovian jumping Lur’e systems (MJLSs) over the finite-time interval. The partial accessibility of system modes with respect to the designed controller is described by a hidden Markov model (HMM). The asynchronous control law consists of two parts, i.e., the states and the nonlinearities involved in the dynamics of the controlled system. By selecting the appropriate Lyapunov functional and applying the modified sector condition, the finite-time stabilization conditions under the control constraints are derived. Finally, the effectiveness of the designed method is verified by an illustrative simulation. [ABSTRACT FROM AUTHOR]

The problem of finite-time path following control for a typical 6-DOF (degree of freedom) autonomous underwater vehicle (AUV) subjected to parametric and modeling uncertainties, disturbances and unknown saturation nonlinearities is studied and discussed in this article. For the mentioned AUV, finite-time control inputs are designed based on innovative terminal sliding surfaces and several finite-time adaptation laws. By means of the designed adaptation laws, the unknown physical parameters of AUVs, the unknown upper bound of uncertainties, and an unknown parameter of input saturation are estimated. By using the Lyapunov stability theorem, it is proven that designed control inputs are able to ensure and provide the practical finite-time stability for the closed-loop AUV system. Furthermore, it is mathematically demonstrated that the tracking errors (defined for the path following problem of the AUV) converge to the vicinity of zero within an adjustable finite time. Finally, the efficacy of the suggested control scheme is demonstrated by the hardware-in-the-loop OPAL real-time test. [ABSTRACT FROM AUTHOR]

This article proposes a black-box behavioral modeling framework for analog circuit blocks (CBs) operating under small-signal conditions around nonstationary operating points. Such variations may be induced either by changes in the loading conditions or by event-driven updates of the operating point for system performance optimization, e.g., to reduce power consumption. An extension of existing data-driven parameterized reduced-order modeling techniques is proposed, which considers the time-varying bias components of the port signals as nonstationary parameters. These components are extracted at runtime by a low-pass filter and used to instantaneously update the matrices of the reduced-order state-space model realized as a SPICE netlist. Our main result is a formal proof of quadratic stability of such linear parameter varying (LPV) models, enabled by imposing a specific model structure and representing the transfer function in a basis of positive functions whose elements constitute a partition of unity. The proposed quadratic stability conditions are easily enforced through a finite set of small-size linear matrix inequalities (LMIs), used as constraints during model construction. Numerical results on various CBs, including voltage regulators, confirm that our approach not only ensures the model stability but also provides speedup in runtime up to two orders of magnitude with respect to full transistor-level circuits. [ABSTRACT FROM AUTHOR]

In this article, the stability and global dissipativity for neutral-type fuzzy genetic regulatory networks (FGRNs) with mixed time delays are investigated. By using Lyapunov functional method and linear matrix inequalities (LMIs) techniques, new sufficient conditions ensuring the stability and global dissipativity of the considered system are given. Moreover, the globally attractive set and positive invariant set are also presented here. The derived criteria are of the form of LMI and they can be checked by the numerically effect Matlab LMI toolbox. Lastly, two numerical examples with its simulations are proposed to illustrate the effectiveness of the obtained results. The derived results of this article are new and complement many earlier works and the ideas of this work can be applied to investigate other similar systems. [ABSTRACT FROM AUTHOR]

SUMMARY: This paper addresses robust stability and position tracking problems in teleoperation systems subject to varying delay in the communication medium, uncertainties in the models of manipulators, and non-passive interaction forces in the terminations. Fixed-structure nonlinear control law is developed based on the notion of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) scheme. Then, utilizing the Lyapunov–Krasovskii theorem, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) to tune the controller parameters. Differently from literature, the objectives are achieved without requirement for any passive parts in the model of interaction forces. Comparative simulations and experimental results demonstrate the applicability and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the local asymptotic stability problem for a competitive Lotka–Volterra system with time-varying delays. By constructing the novel augmented Lyapunov–Krasovskii functionals and using the Wirtinger integral inequality, some alternative stability criteria are obtained by means of linear matrix inequalities. In particular, our constructed functionals contain some cross terms related to four different time delays. The proposed stability conditions in this paper are less conservative as compared with the most existing ones due to using some advanced techniques. Finally, a numerical example illustrates the effectiveness and improvement of the obtained results.