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Path-Complete Lyapunov Functions for Continuous-Time Switching Systems

Abstract : We use a graph-theory-based argument to propose a novel Lyapunov construction for continuous-time switching systems. Starting with a finite family of continuously differentiable functions, the inequalities involving these functions and the vector fields of the switching system are encoded in a direct and labeled graph. Relaying on the (path-)completeness of this graph, we introduce a signal-dependent Lyapunov function, providing sufficient conditions for stability under fixed-time or dwell-time switching hypothesis. For the case of linear systems, our conditions turn into linear matrix inequalities (LMI), and thus they are compared with previous results, via numerical examples .
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https://hal.archives-ouvertes.fr/hal-02971179
Contributor : Matteo Della Rossa <>
Submitted on : Monday, October 19, 2020 - 11:57:10 AM
Last modification on : Wednesday, November 4, 2020 - 3:16:04 PM

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  • HAL Id : hal-02971179, version 1

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Matteo Della Rossa, Mirko Pasquini, David Angeli. Path-Complete Lyapunov Functions for Continuous-Time Switching Systems. 59th Conference on Decision and Control (CDC) 2020, Dec 2020, Jeju Island (virtual conference), South Korea. ⟨hal-02971179⟩

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