Path-Complete Lyapunov Functions for Continuous-Time Switching Systems

Matteo Della Rossa (1) , Mirko Pasquini (2, 3) , David Angeli (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 Imperial College London
3 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence

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 .

Domaines: Automatique / Robotique; Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

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. ⟨10.1109/CDC42340.2020.9304192⟩. ⟨hal-02971179⟩