Constructions of strict Lyapunov functions for discrete time and hybrid time-varying systems

被引：16
|
作者：
Malisoff, Michael [1 ]
Mazenc, Frederic [2 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] UMR Anal Syst & Biomet INRA, Projet MERE INRIA INRA, F-34060 Montpellier, France
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2008年 / 2卷 / 02期
基金：
美国国家科学基金会;
关键词：
Strict Lyapunov functions; Discrete and hybrid time-varying systems;
D O I：
10.1016/j.nahs.2006.12.005
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov's Theorem. We use our methods to build strict Lyapunov functions for time-varying hybrid systems that contain mixtures of continuous and discrete time evolutions. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：394 / 407
页数：14
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