Asian-European Journal of Mathematics Vol. 5, No. 2 (2012) 1250025 (12 pages) c  World Scientific Publishing Company DOI: 10.1142/S1793557112500258 A SWITCHING RULE FOR THE ASYMPTOTIC STABILITY OF DISCRETE-TIME SYSTEMS WITH CONVEX POLYTOPIC UNCERTAINTIES Kreangkri Ratchagit Department of Mathematics, Maejo University Chiangmai 50290, Thailand kreangkri@mju.ac.th Communicated by J. Pecarfic Received October 19, 2011 Revised November 1, 2011 Published July 27, 2012 This paper addresses the stability for a class of linear delay-difference equations with interval time-varying delays. Based on the parameter-dependent Lyapunov–Krasovskii functional, new delay-dependent conditions for the stability are established in terms of linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of our results. Keywords : Switching design; convex polytopic uncertainties; discrete system; asymptotic stability; Lyapunov function; linear matrix inequality. AMS Subject Classification: 47N10, 93C55, 93D20, 94C10 1. Introduction As an important class of hybrid systems, switched systems arise in many practical processes that cannot be described by exclusively continuous or exclusively discrete models, such as manufacturing, communication networks, automotive engineering control and chemical processes (see, e.g. [5, 8, 9] and the references therein). 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. By using the Floquet theory, the author gives a new sufficient conditions for stabilizability in terms of a controllability rank condi- tion for a linear time-invariant discretized system as well as of matrix inequalities in [7]. During the last decades, the stability analysis of switched linear contin- uous/discrete time-delay systems has attracted a lot of attention [2, 3, 6, 11]. The main approach for stability analysis relies on the use of Lyapunov–Krasovskii 1250025-1