Smooth Approximation of Patchy Lyapunov Functions for Switched Systems

Matteo Della Rossa 1 Aneel Tanwani 1 Luca Zaccarian 1, 2
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : Starting with a locally Lipschitz (patchy) Lyapunov function for a given switched system, we provide the construction of a continuously differentiable (smooth) Lyapunov function, obtained via a convolution-based approach. This smooth function approximates the patchy function when working with Clarke's generalized gradient. The convergence rate inherited by the smooth approximations, as a by-product of our construction, is useful in establishing the robustness with respect to additive inputs. With the help of an example, we address the limitations of our approach for other notions of directional derivatives, which generally provide less conservative conditions for stability of switched systems than the conditions based on Clarke's generalized gradient.
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Submitted on : Friday, July 19, 2019 - 11:57:19 AM
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Matteo Della Rossa, Aneel Tanwani, Luca Zaccarian. Smooth Approximation of Patchy Lyapunov Functions for Switched Systems. 11th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2019), Sep 2019, Vienne, Austria. ⟨hal-02189280⟩

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