中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30505-030505.doi: 10.1088/1674-1056/19/3/030505

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Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

党创寅1, 于永斌2, 张洪斌3, 夏建伟4   

  1. (1)Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong; (2)School of Computer Science & Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China; (3)School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China;Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong; (4)School of Mathematics Science, Liaocheng University, Liaocheng 252000, China
  • 收稿日期:2008-09-04 修回日期:2009-07-09 出版日期:2010-03-15 发布日期:2010-03-15
  • 基金资助:
    Project partially supported by the grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No.~101005), the National Natural Science Foundation of China (Grant No.~60904004), the Key Youth Science and Technology Foundation of University of Electronic Science and Technology of China (Grant No.~L08010201JX0720).

Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

Zhang Hong-Bin(张洪斌) a)d), Xia Jian-Wei(夏建伟)b), Yu Yong-Bin(于永斌)c), and Dang Chuang-Yin(党创寅)d)   

  1. a School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China; b School of Mathematics Science, Liaocheng University, Liaocheng 252000, China; c School of Computer Science & Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China; d Manufacturing Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong
  • Received:2008-09-04 Revised:2009-07-09 Online:2010-03-15 Published:2010-03-15
  • Supported by:
    Project partially supported by the grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No.~101005), the National Natural Science Foundation of China (Grant No.~60904004), the Key Youth Science and Technology Foundation of University of Electronic Science and Technology of China (Grant No.~L08010201JX0720).

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摘要： This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.

Abstract: This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.

Key words: chaos, Chua's circuit, piecewise quadratic Lyapunov functions, synchronisation

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems) 02.10.Yn (Matrix theory) 02.30.Yy (Control theory) 84.30.Bv (Circuit theory)