期刊
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
卷 351, 期 4, 页码 1831-1865出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2014.01.002
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资金
- ANR Grant CHASLIM [ANR-11-BS03-0007]
- CONACyT(Mexico) - CNRS (France) [190776]
- Programa de Apoyo a Proyectos de Investiagacion e Inovacion Tecnologico (PAPIIT) 113613 of UNAM [CONACyT 132125]
- Agence Nationale de la Recherche (ANR) [ANR-11-BS03-0007] Funding Source: Agence Nationale de la Recherche (ANR)
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. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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