Science in China Series F: Information Sciences

, Volume 51, Issue 3, pp 283–292

Globally exponentially attractive sets of the family of Lorenz systems

  • Liao XiaoXin 
  • Fu YuLi 
  • Xie ShengLi 
  • Yu Pei 
Article

DOI: 10.1007/s11432-008-0024-2

Cite this article as:
Liao, X., Fu, Y., Xie, S. et al. Sci. China Ser. F-Inf. Sci. (2008) 51: 283. doi:10.1007/s11432-008-0024-2

Abstract

In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b → 1+ and a → 0+, for which the previous methods failed, have been solved using a unified formula.

Keywords

the family of Lorenz systemsglobally exponentially attractive setLagrange stabilitygeneralized Lyapunov function

Copyright information

© Science in China Press 2008

Authors and Affiliations

  • Liao XiaoXin 
    • 1
    • 2
  • Fu YuLi 
    • 3
  • Xie ShengLi 
    • 3
  • Yu Pei 
    • 4
  1. 1.Department of Control Science & EngineeringHuazhong University of Science & TechnologyWuhanChina
  2. 2.School of AutomationWuhan University of Science & TechnologyWuhanChina
  3. 3.School of Electronics & Information EngineeringSouth China University of TechnologyGuangzhouChina
  4. 4.Department of Applied MathematicsThe University of Western Ontario LondonCanada