中国物理B ›› 2008, Vol. 17 ›› Issue (12): 4407-4417.doi: 10.1088/1674-1056/17/12/013

• GENERAL • 上一篇    下一篇

Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty

马铁东, 张化光, 浮洁   

  1. School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
  • 收稿日期:2008-06-02 修回日期:2008-07-07 出版日期:2008-12-20 发布日期:2008-12-20
  • 基金资助:
    Project supported by the National Natural Science foundation of China (Grant Nos 60534010, 60572070, 60774048 and 60728307), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No 60521003) and the National High Technolog

Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty

Ma Tie-Dong (马铁东), Zhang Hua-Guang (张化光), Fu Jie (浮洁)   

  1. School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
  • Received:2008-06-02 Revised:2008-07-07 Online:2008-12-20 Published:2008-12-20
  • Supported by:
    Project supported by the National Natural Science foundation of China (Grant Nos 60534010, 60572070, 60774048 and 60728307), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No 60521003) and the National High Technolog

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摘要： This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur'e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur'e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi--perturbation chaotic Lur'e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Abstract: This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur'e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur'e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi--perturbation chaotic Lur'e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Key words: chaotic Lur'e systems, exponential synchronization, time-varying delay, parametric uncertainty

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.50.Ey (Stochastic processes) 05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)