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This paper is concerned with asynchronous finite-time H ∞ control for a class of discrete-time switched linear systems via admissible edge-dependent average dwell time (AED-ADT) approach. Firstly, by considering the switching time delay between the system and the state feedback controller, appropriate Lyapunov functions are constructed for asynchronous and synchronous switching, respectively. Secondly, for the existence of a set of state feedback controllers, a sufficient condition which guarantees the finite-time boundedness of the closed-loop system with AED-ADT is proposed. Thirdly, a sufficient condition for finite-time H ∞ control with a prescribed H ∞ performance is further developed based on the obtained result. Finally, a numerical example is given to verify the validity of the proposed theoretical results. [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]

In this paper, the finite-frequency fault detection filter design for discrete-time switched systems is investigated. The frequencies of the faults and the unknown disturbance input are assumed to be finite and in three known intervals, qualified as low-, middle-, and high-frequency intervals. Based on the switched Lyapunov function and the generalized Kalman-Yakubovic-Popov lemma, efficient conditions are obtained to guarantee the existence of a finite-frequency fault detection filter, such that the error system is asymptotically stable with an H∞/H- performance index. Finally, a chemical reactor control system is employed to illustrate the obtained techniques.

In this paper, the problem of l2-l∞ control is investigated for the sampled-data systems including packet dropout. The sampled-data system is modeled as a discrete-time switched system based on the number of lost packets. Then the controller is designed to guarantee the discrete-time switched system is exponentially stable with a prescribed l2-l∞ performance subject to mode dependent average dwell time approach. The sufficient conditions to solve the controller gain is derived via a set of linear matrix inequalities (LMIs). Finally, an example is presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered H ∞ filtering problem for discrete-time switched linear systems is addressed. The filter and the system are connected via a communication network, and the transmitted information of system output and switching signal is determined by an event-triggered transmission scheme, which contains system mode dependent parameters. Consequently, the asynchronous switching between the filter and the system occurs, and the filtering error system is modeled as a switched system with augmented switching signal by using the merging switching signal technique. Then, by the multiple Lyapunov function method, a new sufficient condition is obtained such that the filtering error system is exponentially asymptotically stable and satisfies the weighted H ∞ performance. Finally, the design method for the filter and event-triggered parameters is proposed by solving a set of linear matrix inequalities. Numerical simulations illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of actuator fault estimation and accommodation for discrete-time switched systems with state delay. By using reduced-order observer method and switched Lyapunov function technique, a fault estimation algorithm is achieved for the discrete-time switched system with actuator fault and state delay. Then based on the obtained online fault estimation information, a switched dynamic output feedback controller is employed to compensate for the effect of faults by stabilizing the closed-loop systems. Finally, an example is proposed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This study is concerned with the generalised ℋ2 fault detection problem for a class of discrete‐time switched systems with repeated scalar non‐linearities. To reduce the overdesign of the quadratic framework, this study proposes a switching‐sequence‐dependent Lyapunov function approach to the fault detection filter design procedure. Sufficient conditions are obtained for the existence of admissible generalised ℋ2 fault detection filter. Since these conditions involve matrix equalities, the cone complementarity linearisation procedure is employed to cast the non‐convex feasibility problem into a sequential minimisation problem subject to linear matrix inequalities, which can be readily solved by using the standard numerical software. If these conditions are feasible, a desired fault detection filter can be easily constructed. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory. [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]

In this paper, the event-triggered H ∞ filtering problem for discrete-time switched linear systems is addressed. The filter and the system are connected via a communication network, and the transmitted information of system output and switching signal is determined by an event-triggered transmission scheme, which contains system mode dependent parameters. Consequently, the asynchronous switching between the filter and the system occurs, and the filtering error system is modeled as a switched system with augmented switching signal by using the merging switching signal technique. Then, by the multiple Lyapunov function method, a new sufficient condition is obtained such that the filtering error system is exponentially asymptotically stable and satisfies the weighted H ∞ performance. Finally, the design method for the filter and event-triggered parameters is proposed by solving a set of linear matrix inequalities. Numerical simulations illustrate the effectiveness of the proposed approach., (Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.)