Sufficient and necessary conditions for Lyapunov stability of Lorenz system and their application

The sufficient and necessary conditions for Lyapunov stability of the zero equilibrium point of Lorenz system are discussed, and some brief criteria are presented for globally exponential stability, globally asymptotical stability and instability. Furthermore, the behavior of the non-zero equilibriu...

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Bibliographic Details
Published in:Science China. Information sciences 2010-08, Vol.53 (8), p.1574-1583
Main Authors: Luo, Qi, Liao, XiaoXin, Zeng, ZhiGang
Format: Article
Language:English
Subjects:
Asymptotic properties
China
Computer Science
Control systems
Control theory
Criteria
Information Systems and Communication Service
Instability
Laws
Lorenz system
Lorenz系统
Lyapunov稳定
Research Papers
Stability
Theorems
充分必要条件
全局指数稳定性
全局渐近稳定
李雅普诺夫
混沌控制系统
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Summary:The sufficient and necessary conditions for Lyapunov stability of the zero equilibrium point of Lorenz system are discussed, and some brief criteria are presented for globally exponential stability, globally asymptotical stability and instability. Furthermore, the behavior of the non-zero equilibrium point of Lorenz system is also investigated, and several sufficient and necessary conditions are provided for locally exponential stability and instability. The established theorems in this paper develop and extend the existing achievements on Lyapunov stability of Lorenz system. In conclusion, by applying the obtained results, some less conservative feedback-control laws are derived to guarantee the globally exponential stability of the chaos control of then system, Lii system, Yang-Chen system and Yu-Xia Li system.
ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-010-4032-7