Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251) Pub Date : 1999-12-10 DOI:10.1109/ACC.1999.782317

V. Chellaboina, A. Leonessa, W. M. Haddad

引用次数: 37

Abstract

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.

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非线性动力系统的广义Lyapunov定理和不变集定理

本文给出了非线性动力系统的广义Lyapunov定理和不变集定理，其中去除了Lyapunov函数和系统动力学上的所有正则性假设。特别地，利用下半连续李雅普诺夫函数给出了局部稳定性定理和全局稳定性定理。进一步，导出了广义不变集定理，其中系统轨迹收敛于包含在广义李雅普诺夫水平曲面闭包的有限区间内的交集中的最大不变集的并。所提出的结果提供了标准李雅普诺夫定理和不变集定理的透明推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)

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