Finite-time and fixed-time stabilization: Implicit Lyapunov function approach. (January 2015)

• Record Type: Journal Article
• Authors: Polyakov, Andrey; Efimov, Denis; Perruquetti, Wilfrid
• Is Part Of: Automatica. Volume 51(2015)
• Page Start: 332
• Page End: 340
• Publication Date: 2015-01
• Subjects: Lyapunov methods -- Robust control -- Sliding mode control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2014.10.082
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: Theorems on Implicit Lyapunov Functions (ILF) for finite-time and fixed-time stability analysis of nonlinear systems are presented. Based on these results, new nonlinear control laws are designed for robust stabilization of a chain of integrators. High order sliding mode (HOSM) algorithms are obtained as particular cases. Some aspects of digital implementations of the presented algorithms are studied, it is shown that they possess a chattering reduction ability. Theoretical results are supported by numerical simulations.