Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces
Falk Hante (IECN, INRIA Lorraine / IECN / MMAS), Mario Sigalotti, (IECN, INRIA Lorraine / IECN / MMAS)
TL;DR
This paper establishes necessary and sufficient conditions for the global exponential stability of switched systems in Banach and Hilbert spaces using common Lyapunov functions, extending classical Lyapunov theorems to infinite-dimensional settings.
Contribution
It introduces Converse Lyapunov Theorems for switched systems in infinite-dimensional spaces, providing a theoretical foundation for stability analysis.
Findings
Necessary and sufficient conditions for stability in Banach and Hilbert spaces
Existence of a common Lyapunov function for all modes
Stability criteria uniform with respect to switching signals
Abstract
We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.
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