Discontinuous Lyapunov Functions for Nonasymptotic Stability Analysis

Andrey Polyakov 1
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : The paper presents mathematical tools required for finite-time stability analysis of discontinuous control systems using discontinuous Lyapunov functions. Elements of Filippov theory of differential equations with discontinuous right-hand sides and stability notions are briefly observed. Concepts of generalized derivatives and non-smooth Lyapunov functions are considered. The generalized Lyapunov theorems for stability analysis and convergence time estimation are presented and supported by examples.
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Andrey Polyakov. Discontinuous Lyapunov Functions for Nonasymptotic Stability Analysis. IFAC World Congress, Aug 2014, Cape Town, South Africa. ⟨hal-00977869⟩

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