Lyapunov functions for time varying systems satisfying generalized conditions of Matrosov theorem
Loading...
Citations
Altmetric:
Altmetric::
Download
Associated Records
File Licence
Editors
Date
2005-01-01
Source Title
Proceedings of the ... IEEE Conference on Decision & Control / IEEE Control Systems Society. IEEE Conference on Decision & Control
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
Melbourne Authors
Affiliation
Electrical and Electronic Engineering
Document Type
Conference Paper
Subject Code
Citation
Mazenc, F. & Nesic, D. (2005). Lyapunov functions for time varying systems satisfying generalized conditions of Matrosov theorem. Proceedings of the 44th IEEE Conference on Decision Control/European Control Conference, Vols. 1-8, 2005, pp.5432-5437. IEEE. https://doi.org/10.1109/CDC.2005.1583026.
Access Status
Open Access
Access URL
Open Access URL
Open Access at PMC
Linked Resource URL
NHMRC Grant Code
ARC Grant Code
Description
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.