Stability and Stabilization for Discrete Systems with Time-Delay

Abstract

Recently, much attention has been given to the delay-dependent stability and stabilization of continuous systems with time-delay, see for example,[146, 139, 99, 44, 188, 53, 109, 185, 78, 198, 203]. In those papers, many kinds of Lyapunov-Krasovskii functional are proposed in order to derive less conservative stability conditions. Correspondingly, some of the techniques adopted in the above papers have been extended to the stability and stabilization problem for discrete systems with time-delay. Less conservative stability conditions for discrete systems with time-delay are also derived, see, [53, 201] for example. However, discrete system with time-delay has an important feature, that is, it can be transformed into augmented delay-free system [3, 170]. Then, the stability and stabilization of such a system can be solved with a simple Lyapunov function. Although the dimensions of augmented systems could be larger if the time-delay is large, the stability conditions are simple and convex, which can be checked easily by today’s fast developing computing techniques.