Stability notions and Lyapunov functions for sliding mode control systems

Stability notions and Lyapunov functions for sliding mode control systems

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 (...

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Veröffentlicht in:Journal of the Franklin Institute 2014-04, Vol.351 (4), p.1831-1865
Hauptverfasser: Polyakov, Andrey, Fridman, Leonid
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Sprache:eng
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Automatic Control Engineering
Computer Science
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container_title Journal of the Franklin Institute
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creator Polyakov, Andrey
Fridman, Leonid
description 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.
doi_str_mv 10.1016/j.jfranklin.2014.01.002
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subjects Automatic Control Engineering
Computer Science
title Stability notions and Lyapunov functions for sliding mode control systems
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