NDLI: Lyapunov functions for time varying systems satisfying generalized conditions of Matrosov theorem

Content Provider	IEEE Xplore Digital Library
Author	Mazenc, F. Nesic, D.
Copyright Year	2005
Description	Author affiliation: Projet MERE INRIA-INRA, UMR LASB, INRA 2, pl. Viala, 34 060 Montpellier, France, Frederic.Mazenc@ensam.inra.fr (Mazenc, F.)
Abstract	The classical Matrosov theorem concludes uniform asymptotic stability of time varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semi-definite derivative along solutions) and another auxiliary function with derivative that is strictly non-zero where the derivative of the Lyapunov function is zero [10]. Recently, several generalizations of the classical Matrosov theorem that use a finite number of Lyapunov-like functions have been reported in [5]. None of these results provides a construction of a strong Lyapunov function (positive definite, decrescent, with negative definite derivative along solutions) that is a very useful analysis and controller design tool for nonlinear systems. Inspired by generalized Matrosov conditions in [5], we provide a construction of a strong Lyapunov function via an appropriate weak Lyapunov function and a set of Lyapunov-like functions whose derivatives along solutions of the system satisfy a particular triangular structure. Our results will be very useful in a range of situations where strong Lyapunov functions are needed, such as robustness analysis and Lyapunov function based controller redesign.
Starting Page	5432
Ending Page	5437
File Size	140696
Page Count	6
File Format	PDF
ISBN	0780395670
DOI	10.1109/CDC.2005.1583026
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-15
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	IEEE/EUCA
Subject Keyword	Time varying systems Lyapunov method Asymptotic stability Nonlinear systems Robust control Robust stability Control system analysis Nonlinear control systems Control systems Stability analysis Time-Varying Lyapunov functions Matrosov Theorem Nonlinear Stability
Content Type	Text
Resource Type	Article

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