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This paper investigates the output-feedback control for discrete-time switched linear systems. By extending the methodology of switched Lyapunov functions (SLF), a non-monotonic SLF approach is proposed to analyse the stability of the resulting closed-loop system under arbitrary switching. This approach relaxes the requirement of monotonicity to conventional SLF approach, and hence it will lead to less conservative results. First, the stability of discrete-time switched systems is analysed, and then an output-feedback controller design method is proposed based on the obtained stability results. The controller design problem is formulated in term of LMIs, and relaxed variables are introduced in the synthesis conditions to improve the design freedom. Finally, three examples are used to verify the effectiveness and application potential of the proposed methods. [ABSTRACT FROM AUTHOR]

We study the stability of discrete-time switched systems for any laws of switching between linear subsystems. Pairwise connected systems are distinguished among such systems. A sufficient frequency-domain stability condition has been obtained for them. Two sufficient conditions and two criteria for the existence of a Lyapunov quadratic function are obtained for switched systems whose stability is equivalent to the absolute stability of Lur'e systems with two nonlinearities. These conditions amount to checking the solvability of special matrix inequalities whose dimensions are considerably lower than the dimension of the original system of matrix inequalities that defines the necessary and sufficient conditions. The resulting conditions are compared with the conditions of the Tsypkin criterion and with the necessary and sufficient conditions using the examples of systems of the third and sixth orders. [ABSTRACT FROM AUTHOR]

The event-triggered control problem for discrete-time switched linear systems with packet losses is addressed in this paper. It is assumed that, at each event-triggered instant transmitted successfully, the controller can only access the transmitted information of system state and mode. In both cases of packet losses and no packet losses, mode dependent event-triggered transmission schemes are proposed. And the closed-loop system is modeled as a switched system with augmented switching signal. Then, based on the multiple Lyapunov function method, in the case of packet losses, exponential stability conditions are given with constraint of the maximum allowable number of successive packet losses, and design methods for state feedback controller gains and mode dependent event-triggered parameters are obtained. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

The problem of stability is studied in this paper for a class of discrete-time switched systems with unstable subsystems. Two new definitions of slow switching and fast switching on the basis of admissible edge-dependent average dwell time are proposed, respectively. Some conditions are established by using multiple Lyapunov function method to guarantee the global uniform exponential stability of discrete-time switched systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The problems of stability and l 2 − l ∞ filtering are studied in this paper for a class of discrete-time switched systems. A novel admissible edge-dependent average dwell time switching is proposed on the basis of the directed graph. A condition ensuring the global uniform exponential stability of discrete-time switched systems is established. A new inequality that depicted the relation between Lyapunov-like function and disturbances is presented to guarantee the l 2 − l ∞ performance. Combined with the multiple Lyapunov-like function technology, the filtering error system is proved to be globally uniformly exponentially stable with l 2 − l ∞ performance, and the corresponding filter can also be obtained. Finally, three numerical examples are illustrated to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of actuator fault estimation observer design for discrete-time switched systems with finite-frequency. The frequencies of the fault and the unknown input disturbance are assumed to be in a finite range. A finite frequency fault estimation observer is proposed to estimate the actuator fault in the entire frequency domain. Based on the generalized Kalman–Yakubovic–Popov (KYP) lemma and the switched Lyapunov function method, the efficient conditions are obtained to achieve the fault estimation observer design. Finally, an example is given to illustrate the proposed technique. [ABSTRACT FROM AUTHOR]

The problem of observer-based finite-time exponential l2 − l∞ control is studied in this paper for a class of discrete-time switched systems with time delay and uncertainties. The observer-based controller is designed to guarantee that the developed closed-loop system is robust finite-time exponential l2 − l∞ stabilizable for all admissible uncertainties. By resorting to the average dwell time approach and Lyapunov–Krasovskii functional technology, some new delay-dependent criteria guaranteeing finite-time boundedness and stabilizability with exponential l2 − l∞ performance are developed. The observer-based finite-time exponential l2 − l∞ controller is also designed by virtue of a cone complement linearization method. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers the design of robust H∞ filtering problem for switched stochastic discrete time-delay system with missing measurements via switched Lyapunov function approach. Attention is focused on the design of an exponentially stable filter guaranteeing a prescribed noise attenuation level in the H∞ sense and missing measurements probability. By using switched Lyapunov functionals, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of delay-dependent filtering for a class of discrete-time switched systems with state delays is investigated under arbitrary switching using a parametrized approach. Attention is focused on the design of asymptotically stable filter guaranteeing a prescribed noise attenuation level in the sense. By using switched Lyapunov functionals, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs), the solution of which constructs the desired filter under arbitrary switching. Numerical examples are provided to demonstrate the effectiveness of the proposed techniques. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problems of robust stability, robust stabilization and H ∞ control via memoryless state feedback for uncertain discrete-time switched systems with mode-dependent time delays. Based on linear matrix inequalities (LMIs), a descriptor model transformation of the system and a switched Lyapunov function, new delay-dependent criteria are established which are not contained in known literatures. Numerical examples are presented to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]