Brief paper: Razumikhin-type stability theorems for discrete delay systems

Authors:
Bin Liu;Horacio J. Marquez
Affiliations:
Department of Information and Computation Sciences, Hunan University of Technology, Zhuzhou 412008, China;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2V4
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

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.