中国物理B ›› 2008, Vol. 17 ›› Issue (7): 2377-2387.doi: 10.1088/1674-1056/17/7/010

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Impulsive control of nonlinear systems with time-varying delays

廖晓峰1, 于永斌2, 鲍景富2, 张洪斌2, 钟其水2, 虞厥邦2   

  1. (1)College of Computer Science, Chongqing University, Chongqing 400044, China; (2)College of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
  • 收稿日期:2007-10-08 修回日期:2007-12-10 出版日期:2008-07-09 发布日期:2008-07-09

Impulsive control of nonlinear systems with time-varying delays

Yu Yong-Bin(于永斌)a)†, Bao Jing-Fu(鲍景富)a), Zhang Hong-Bin(张洪斌)a), Zhong Qi-Shui(钟其水)a), Liao Xiao-Feng(廖晓峰)b), and Yu Jue-Bang(虞厥邦)a)   

  1. a College of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China; b College of Computer Science, Chongqing University, Chongqing 400044, China
  • Received:2007-10-08 Revised:2007-12-10 Online:2008-07-09 Published:2008-07-09

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摘要： A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

关键词: impulsive control, time-varying delays, impulsive delay systems, Lyapunov functions

Abstract: A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

Key words: impulsive control, time-varying delays, impulsive delay systems, Lyapunov functions

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

  • 05.45.Gg
02.30.Yy (Control theory) 05.45.Pq (Numerical simulations of chaotic systems) 05.45.Tp (Time series analysis)