Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

被引：22
|
作者：
Chellaboina, V
Leonessa, A
Haddad, WM [1 ]
机构：
[1] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA
[2] Univ Missouri, Dept Mech & Aerosp Engn, Columbia, MO 65211 USA
来源：
SYSTEMS & CONTROL LETTERS | 1999年 / 38卷 / 4-5期
基金：
美国国家科学基金会;
关键词：
generalized Lyapunov functions; invariant set theorems; nonlinear dynamical systems; lower semicontinuous Lyapunov functions;
D O I：
10.1016/S0167-6911(99)00076-6
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems. (C) 1999 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：289 / 295
页数：7
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