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Razumikhin-type stability theorems for discrete delay systems. (English) Zbl 1123.93065
Summary: 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.

MSC:
93C55 Discrete-time control/observation systems
34K20 Stability theory of functional-differential equations
93D30 Lyapunov and storage functions
93D20 Asymptotic stability in control theory
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