中国物理B ›› 2009, Vol. 18 ›› Issue (5): 1774-1779.doi: 10.1088/1674-1056/18/5/010

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Fuzzy modeling and impulsive control of hyperchaotic Lü system

李东1, 张小洪2   

  1. (1)College of Mathematics & Physics, Chongqing University, Chongqing 400030, China; (2)School of Software Engineering, Chongqing University, Chongqing 400030, China
  • 收稿日期:2008-10-07 修回日期:2008-11-01 出版日期:2009-05-20 发布日期:2009-05-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60604007).

Fuzzy modeling and impulsive control of hyperchaotic Lü system

Zhang Xiao-Hong(张小洪)a)† and Li Dong(李东)b)   

  1. a School of Software Engineering, Chongqing University, Chongqing 400030, China; b College of Mathematics & Physics, Chongqing University, Chongqing 400030, China
  • Received:2008-10-07 Revised:2008-11-01 Online:2009-05-20 Published:2009-05-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60604007).

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摘要： This paper presents a novel approach to hyperchaos control of hyperchaotic systems based on impulsive control and the Takagi--Sugeno (T--S) fuzzy model. In this study, the hyperchaotic Lü system is exactly represented by the T--S fuzzy model and an impulsive control framework is proposed for stabilizing the hyperchaotic Lü system, which is also suitable for classes of T--S fuzzy hyperchaotic systems, such as the hyperchaotic R?ssler, Chen, Chua systems and so on. Sufficient conditions for achieving stability in impulsive T--S fuzzy hyperchaotic systems are derived by using Lyapunov stability theory in the form of the linear matrix inequality, and are less conservative in comparison with existing results. Numerical simulations are given to demonstrate the effectiveness of the proposed method.

关键词: hyperchaos control, impulsive control, T--S fuzzy model, linear matrix inequalities

Abstract: This paper presents a novel approach to hyperchaos control of hyperchaotic systems based on impulsive control and the Takagi--Sugeno (T--S) fuzzy model. In this study, the hyperchaotic Lü system is exactly represented by the T--S fuzzy model and an impulsive control framework is proposed for stabilizing the hyperchaotic Lü system, which is also suitable for classes of T--S fuzzy hyperchaotic systems, such as the hyperchaotic R?ssler, Chen, Chua systems and so on. Sufficient conditions for achieving stability in impulsive T--S fuzzy hyperchaotic systems are derived by using Lyapunov stability theory in the form of the linear matrix inequality, and are less conservative in comparison with existing results. Numerical simulations are given to demonstrate the effectiveness of the proposed method.

Key words: hyperchaos control, impulsive control, T--S fuzzy model, linear matrix inequalities

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Pq (Numerical simulations of chaotic systems)