Razumikhin-type stability theorems for discrete delay systems

In this paper. by employing the Razumikhin technique and Lyapunov functions, Razumikhin-type theorems that guarantee the uniform stability, uniformly asymptotic stability and uniformly exponential stability for the general discrete delay systems are established, respectively. Moreover, Razumikhin-type uniformly exponential stability theorem gives the estimation of the convergence speed. As theoretic application, the Razumikhin-type uniformly exponential stability result is further studied and used to show some well-known stability results for some kinds of discrete delay systems. Finally, examples are also worked through to illustrate our results. Crown Copyright (c) 2007 Published by Elsevier Ltd. All rights reserved.