Stability notions and Lyapunov functions for sliding mode control systems

作者：Polyakov, Andrey^*; Fridman, Leonid

来源：Journal of the Franklin Institute, 2014, 351(4): 1831-1865.

DOI：10.1016/j.jfranklin.2014.01.002

• FINITE-TIME STABILITY
• ORDER

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.

• 出版日期2014-4