中国物理B ›› 2011, Vol. 20 ›› Issue (5): 50508-050508.doi: 10.1088/1674-1056/20/5/050508

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Impulsive control of chaotic systems and its applications in synchronization

吴波1, 刘洋1, 卢剑权2   

  1. (1)College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China; (2)Department of Mathematics, Southeast University, Nanjing 210096, China
  • 收稿日期:2010-08-04 修回日期:2011-01-10 出版日期:2011-05-15 发布日期:2011-05-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10926066 and 11026182), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6100007), the Zhejiang Educational Committee, China (Grant No. Y200805720), th

Impulsive control of chaotic systems and its applications in synchronization

Wu Bo(吴波)a), Liu Yang(刘洋) a)†, and Lu Jian-Quan(卢剑权)b)c)   

  1. a College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China; b Department of Mathematics, Southeast University, Nanjing 210096, China; b Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
  • Received:2010-08-04 Revised:2011-01-10 Online:2011-05-15 Published:2011-05-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10926066 and 11026182), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6100007), the Zhejiang Educational Committee, China (Grant No. Y200805720), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010408), the Innovation Fund of Basic Scientific Research Operating Expenses, China (Grant No. 3207010501), and the Alexander von Humboldt Foundation of Germany.

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摘要： In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.

关键词: comparison systems, impulsive control, chaotic systems, synchronization

Abstract: In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.

Key words: comparison systems, impulsive control, chaotic systems, synchronization

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

  • 05.45.Gg
05.45.Xt (Synchronization; coupled oscillators)