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Journal Articles Journal of The Franklin Institute Year : 2014

Stability notions and Lyapunov functions for sliding mode control systems

Leonid Fridman

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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Dates and versions

hal-00942319 , version 1 (05-02-2014)

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Andrey Polyakov, Leonid Fridman. Stability notions and Lyapunov functions for sliding mode control systems. Journal of The Franklin Institute, 2014, ⟨10.1016/j.jfranklin.2014.01.002⟩. ⟨hal-00942319⟩
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