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Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations. (English) Zbl 1380.93196

Summary: The problem of Finite-Time Stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.

MSC:

93D09 Robust stability
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
93C73 Perturbations in control/observation systems
93D30 Lyapunov and storage functions
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