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Stability analysis of switched multiple nonlinear discrete systems with interval time varying delays

This paper deals with the problem of asymptotic stability for a class of switched nonlineardiscrete systems with time-varying delay. The time-varying delay is assumed to be belong to a given interval in which the lower bound of delay is not restricted to zero. A linear matrix inequality (LMI) approach to asymptotic stability of the system is presented. Based on the Lyapunov functional, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities. | STABILITY ANALYSIS OF SWITCHED MULTIPLE NONLINEAR DISCRETE SYSTEMS WITH INTERVAL TIME-VARYING DELAYS Tran Nguyen Binh∗ , Nguyen Thi Thu Huong, Pham Thi Linh Thai Nguyen University of Economics and Business Administration - Thai Nguyen University ABSTRACT This paper deals with the problem of asymptotic stability for a class of switched nonlineardiscrete systems with time-varying delay. The time-varying delay is assumed to be belong to a given interval in which the lower bound of delay is not restricted to zero. A linear matrix inequality (LMI) approach to asymptotic stability of the system is presented. Based on the Lyapunov functional, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities. Keywords: Switching, discrete systems, uncertainty, Lyapunov function, linear matrix inequality. 1 INTRODUCTION A switched system is a particular kind of hybrid system that consists of several subsystems and a switching law determining at any time instant which subsystem is active. There are indeed many switched systems that occur naturally or by design in the fields of control, communication, computer and signal processes. A different switching rule would cause different behavior of the system and hence lead to different system performances. Because of the complexity of the designing switched law for the systems, the stability analysis and control synthesis of switched systems becomes more difficulty and attracts the interest of several scientists during the last decades [111]. On the other hand, time-delay phenomena are very common in practical systems. A switched system with time-delay individual subsystems is called a switched time-delay system; in particular, when the subsystems are linear, it is then called a switched time-delay linear system. During the past decades, the stability analysis of switched linear continuous/discrete timedelay systems has attracted a lot of attention [48]. The main approach for