Stability notions and Lyapunov functions for sliding mode control systems |
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| Authors: | Andrey Polyakov Leonid Fridman |
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| Institution: | 1. Non-A INRIA - LNE, Parc Scientifique de la Haute Borne 40, avenue Halley Bat.A, Park Plaza, 59650 Villeneuve d′Ascq, France;2. Departamento de Ingenieria de Control y Robotica, UNAM, Edificio T, Ciudad Universitaria D.F., Mexico |
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| 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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