New Delay-Dependent Stabilization Criterion for Time-Delay Chaotic Systems

This paper deals with the problem of standard feedback control for a class of time-delay chaotic systems. A new delay-dependent condition for stabilization with less conservatism is derived in terms of linear matrix inequalities. In order to obtain a lower controller gain, an optimization algorithm is proposed which involves some constraints to restrict the size of gain matrix. A numerical example is provided to show that our method gives significant improvement over the existing ones.

[1]  Keqin Gu Discretized Lyapunov functional for uncertain systems with multiple time-delay , 1999 .

[2]  Oh-Min Kwon,et al.  LMI optimization approach to stabilization of time-delay chaotic systems , 2005 .

[3]  Y. Cao,et al.  Delay-dependent robust stabilization of uncertain systems with multiple state delays , 1998, IEEE Trans. Autom. Control..

[4]  Wolfram Just,et al.  MECHANISM OF TIME-DELAYED FEEDBACK CONTROL , 1996, chao-dyn/9611012.

[5]  C. D. Souza,et al.  Robust exponential stability of uncertain systems with time-varying delays , 1998, IEEE Trans. Autom. Control..

[6]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[7]  Haipeng Peng,et al.  Time-Delayed Feedback Control of Time-Delay Chaotic Systems , 2003, Int. J. Bifurc. Chaos.

[8]  Zhenya He,et al.  Chaotic behavior in first-order autonomous continuous-time systems with delay , 1996 .

[9]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[10]  Jitao Sun Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control , 2004 .

[11]  Guanrong Chen,et al.  On feedback control of chaotic continuous-time systems , 1993 .

[12]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[13]  Guanrong Chen,et al.  On time-delayed feedback control of chaotic systems , 1999 .

[14]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[15]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[16]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[17]  Zhou Luan-jie,et al.  Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems , 2004 .

[18]  Gang Feng,et al.  A full delayed feedback controller design method for time-delay chaotic systems , 2007 .

[19]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[20]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[21]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .