Stability notions and Lyapunov functions for sliding mode control systems

Andrey Polyakov 1 Leonid Fridman 2
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The paper surveys mathematical tools required for stability and convergence analysis of modern sliding mode control systems. Elements of Filippov theory of differential equations with discontinuous right-hand sides and its recent extensions are discussed. Stability notions (from Lyapunov stability (1982) to fixed-time stability (2012)) are 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 from sliding mode control theory.
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Andrey Polyakov, Leonid Fridman. Stability notions and Lyapunov functions for sliding mode control systems. Journal of The Franklin Institute, Elsevier, 2014, ⟨10.1016/j.jfranklin.2014.01.002⟩. ⟨hal-00942319⟩

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