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Exponential stability criteria for discrete time-delay systems. (English) Zbl 1312.93087

Summary: In this paper, we study the exponential stability of linear discrete time-delay systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in Hilbert spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. As an application of the main results, we discuss the exponential stability of a general nonlinear system. The main novelty of this work is that we always consider the exponential behavior of solutions with respect to an specific ball.

MSC:

93D20 Asymptotic stability in control theory
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
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