Abstract
This article is concerned with robust stability of switched discrete time-delay systems with convex polytopic uncertainties. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for robust stability for switched system with convex polytopic uncertainties is designed via linear matrix inequalities. AMS Subject Classification: 47N10, 93C55, 93D20, 94C10
Highlights
Many dynamical systems in real world involve variables that be always confined to the positive orthant, and such systems are generally termed as positive systems in the literature
Many important results have been obtained for switched linear continuous-time systems, there are a few results concerning the stability of switched linear discrete systems with time-varying delays
This paper studies the robust stability problem for switched linear discrete systems with convex polytopic uncertainties with interval time-varying delays
Summary
Many dynamical systems in real world involve variables that be always confined to the positive orthant, and such systems are generally termed as positive systems in the literature. Many important results have been obtained for switched linear continuous-time systems, there are a few results concerning the stability of switched linear discrete systems with time-varying delays. It was shown in [11,12,13,14,15,16,17] that when all subsystems are asymptotically stable, the switching system is asymptotically stable under an arbitrary switching rule. This paper studies the robust stability problem for switched linear discrete systems with convex polytopic uncertainties with interval time-varying delays.
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