中国物理B ›› 2009, Vol. 18 ›› Issue (6): 2176-2183.doi: 10.1088/1674-1056/18/6/011

• GENERAL • 上一篇    下一篇

Pinning control of complex Lur'e networks

张庆振1, 李忠奎2   

  1. (1)School of Automation Science and Electronic Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; (2)State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
  • 收稿日期:2008-08-06 修回日期:2008-09-26 出版日期:2009-06-20 发布日期:2009-06-20

Pinning control of complex Lur'e networks

Zhang Qing-Zhen(张庆振)a)† and Li Zhong-Kui(李忠奎)b)‡   

  1. a School of Automation Science and Electronic Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China; b State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
  • Received:2008-08-06 Revised:2008-09-26 Online:2009-06-20 Published:2009-06-20

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摘要： This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur'e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur'e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua's oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.

Abstract: This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur'e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur'e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua's oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.

Key words: complex dynamical network, Lur'e system, pinning control, linear matrix inequality

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.10.Yn (Matrix theory) 02.30.Yy (Control theory) 05.45.Gg (Control of chaos, applications of chaos) 89.75.Hc (Networks and genealogical trees)