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Linear matrix inequality approach to robust stability of uncertain nonlinear discrete time systems

This paper deals with the problem of asymptotic stability for a class of nonlinear discrete-time 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 constructing improved Lyapunov functionals, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities. A numerical example is given to show the effectiveness of the result | LINEAR MATRIX INEQUALITY APPROACH TO ROBUST STABILITY OF UNCERTAIN NONLINEAR DISCRETE-TIME SYSTEMS Tran Nguyen Binh∗ Thai Nguyen University of Economics and Business Administration - Thai Nguyen University, Vietnam abstract This paper deals with the problem of asymptotic stability for a class of nonlinear discrete-time 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 constructing improved Lyapunov functionals, delay-depenent criteria for the asymptotic stability of the system are established via linear matrix inequalities. A numerical example is given to show the effectiveness of the result Keywords: 1 Stability, discrete systems, uncertainty, Lyapunov function, linear matrix inequality. Introduction The stability analysis of time-delay uncertain systems is a topic of great practical importance, which has attracted a lot of interest over the decades, e.g. see [1, 5, 6]. Also, system uncertainties arise from many sources such as unavoidable approximation, data errors and aging of systems and so the stability issue of uncertain time-delay systems has been investigated by many researchers [5, 6, 7], where the Lyapunov functional method is certainly used as the main tool. However, the conditions obtained in these papers must be solved upon a grid on the parameter space, which results in testing a finite number of linear matrix inequalities (LMIs). In the case, the result using finite griding points are unreliable and the numerical complexity of the tests grows rapidly. In [5,6], to reduce the conservatism of the stability condition the authors proposed a legitimate Lyapunov functional which employs free weighting matrices. To the best of the authors knowledge, the delay-dependent time delay case for the class of discrete-time nonlinear systems with