A Berger-Wang formula for impulsive switched systems
Yacine Chitour (L2S), Jamal Daafouz (IUF, CRAN), Ihab Haidar (ENSEA, LJLL (UMR\_7598), L\'EA), Paolo Mason (L2S), Mario Sigalotti (LJLL (UMR\_7598), CaGE, CNRS, UPCit\'e)
TL;DR
This paper extends the Berger-Wang formula to impulsive switched systems, providing a spectral characterization of their exponential stability by analyzing a related class of weighted discrete-time systems.
Contribution
It introduces a Berger-Wang-type result for impulsive systems, linking their stability to spectral properties, which is a novel extension in switched-systems theory.
Findings
Established a Berger-Wang-type result for weighted discrete-time switched systems
Derived an analogous spectral stability criterion for impulsive systems
Extended existing switched-systems stability results to impulsive dynamics
Abstract
This paper addresses a class of impulsive systems defined by a mix of continuous-time and discrete-time switched linear dynamics. We first analyze a related class of weighted discrete-time switched systems for which we establish a Berger--Wang-type result. An analogous result is then derived for impulsive systems and subsequently used to characterize their exponential stability through a spectral approach, thereby extending existing results in switched-systems theory.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Neural Networks Stability and Synchronization · Advanced Differential Equations and Dynamical Systems