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

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Abstract

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 Chen system, Lü system, Yang-Chen system and Yu-Xia Li system.

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Authors and Affiliations

  1. College of Information and Control, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Qi Luo

  2. Department of Control Science and Engineering, Huazhong University of Science and Technology, Image Processing and Intelligent Control Key Laboratory of Education Ministry of China, Wuhan, 430074, China

    XiaoXin Liao & ZhiGang Zeng

Authors
  1. Qi Luo
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  2. XiaoXin Liao
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  3. ZhiGang Zeng
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Correspondence to Qi Luo.

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Luo, Q., Liao, X. & Zeng, Z. Sufficient and necessary conditions for Lyapunov stability of Lorenz system and their application. Sci. China Inf. Sci. 53, 1574–1583 (2010). https://doi.org/10.1007/s11432-010-4032-7

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  • DOI: https://doi.org/10.1007/s11432-010-4032-7

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