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This study is concerned with the non-fragile mixed ℋ∞/l2 − l∞ synchronisation control problem for discrete-time complex networks with Markov jumping-switching topology under unreliable communication links. The network topology under consideration is assumed to be governed by a Markov chain with time-varying transition probabilities (TPs). The variation of TPs is subject to a kind of slow switching signals; that is, the average dwell time (ADT) switching. The focus is on the design of non-fragile mixed mode-dependent/-independent controllers such that the underlying network reaches stochastic mean-square synchronisation with a mixed ℋ∞/l2 − l∞ performance level for an admissible switching signal with ADT. By using a new mixed ℋ∞/l2 − l∞ performance index, combined with the switched control method, the solutions to the considered problem are formulated. Finally, simulation results demonstrate the effectiveness of our proposed approach.

The problems of finite-time analysis and design for a class of discrete-time switching dynamics Markovian jump linear systems (SD-MJLSs) with time-varying delay are investigated in this study. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition probability matrix, which is subject to a high-level average dwell time (ADT) switching. The time delay is considered as time varying and has a lower and upper bound. First, sufficient conditions, which guarantee the stochastic finite-time boundedness of the underlying systems, are presented by employing the ADT approach. These conditions are not only dependent on the delay upper bound but also the delay range. Then, a finite-time weighted l2 gain of such delay SD-MJLSs is obtained to measure the disturbance attenuation capability over a fixed time interval and the design of the stabilising controller is further given. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. Finally, a numerical example is given to verify the potential of the developed results.

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

A class of nonlinear switched dynamical systems in the presence of impulsive effect, uncertainties and both variable and continuously distributed delays are investigated. By resorting to M-matrix property, inequality technique and the idea of vector Lyapunov function, several sufficient conditions are derived to check the robust exponential stability of the interconnected switched systems under arbitrary switching. The proposed method does not require that each subsystem shares a common Lyapunov function, nor that the value of suitable Lyapunov function at every switching time is known. Moreover, average dwell time approach is employed to obtain criteria for ensuring the global exponential stability of the system under constrained switching. Finally, two numerical examples are presented to demonstrate the correctness and effectiveness of the main results.

This paper deals with the problems of robust exponential stability for a class of uncertain discrete-time switched systems with time-varying delay and linear fractional perturbations parametric uncertainties, under arbitrary switching signal on the one hand and by using the Average Dwell Time (ADT) approach on the other hand. Firstly, new sufficient conditions guaranteeing the exponential stability of the nominal considered system are proposed and proved, by constructing an augmented Lyapunov–Krasovskii functional, by using the discrete Wirtinger-based inequality combined with an improved form of Reciprocally Convex Lemma (RCL) and by considering the two types of switching signal mentioned above. Then, and based on the obtained results, new criteria are established to ensure the robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay. The established conditions are dependent on the lower and the upper delay bounds and are expressed in terms of Linear Matrix Inequalities (LMIs). Furthermore, some slack variables are introduced by using the Finsler lemma in order to give more relaxation for the studied system. Consequently, the proposed approach is proved to have some less conservative results over than some recent works of the literature. Finally, numerical examples are provided to demonstrate the merit and the effectiveness of the proposed approach.

This paper investigates the resilient dynamic output feedback (DOF) control problem for discrete-time descriptor switching Markov jump systems for the first time, where the time-varying transition probabilities are described by a piecewise-constant matrix and a high-level signal subject to average dwell time switching. The controllers to be designed can tolerate additive gain perturbations. Firstly, by constructing a stochastic Lyapunov functional and using an average dwell time method, a sufficient condition is given such that the resultant closed-loop systems are stochastically admissible and have a H ∞ noise attenuation performance. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented such that the resultant closed-loop systems are stochastically admissible with a H ∞ noise attenuation performance. When the uncertain parameters exist not only in plant matrices but also in controller gain matrices, the resilient DOF controller is developed in terms of LMIs, which can be of full order or reduced order. Compared with the previous ones, the proposed design methods do not impose extra constraints on system matrices or slack variables, which show less conservatism. Finally, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.

This paper addresses stabilization problem for a class of switched stochastic systems with time delays by using piecewise Lyapunov–Krasovskii functional method. Asynchronous switching means the switching of the controller has a time delay to the switching of the system. We provide a set of Lyapunov–Krasovskii-type sufficient conditions for establishing the mean-square exponential stability. The mean-square exponential stability condition for the resulting closed-loop system is firstly derived by further allowing the Lyapunov–Krasovskii functional to increase during the running time of the active subsystem with the mismatched controller. Then, the corresponding solvability condition for stabilizing controllers is established. Finally, we present an example to show the effectiveness of the developed theory.