Linear feedback control and synchronization for a new time-delay chaotic system

Base on Lyapunov stability theory of time-delay systems, the chaos control and synchronization problems of time-delay chaotic system are discussed in this paper. A linear controller to realize chaos control is designed and the synchronization problem of a new time-delay chaotic systems is discussed by combining of a new theorem and the characters of the chaotic system. Finally, numerical examples with simulation are provided to illustrate the correctness and effectiveness of the theoretical results.

[1]  Zhongjun Ma,et al.  Generalized synchronization of different dimensional chaotic dynamical systems , 2007 .

[2]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[3]  Guanrong Chen,et al.  Some observer-based criteria for discrete-time generalized chaos synchronization , 2002 .

[4]  Y. Kuramoto,et al.  Dephasing and bursting in coupled neural oscillators. , 1995, Physical review letters.

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

[6]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[7]  Xin Wang,et al.  Linear feedback controller design method for time-delay chaotic systems , 2012 .

[8]  Liu Yong-qing,et al.  Exponential stability of interval dynamical system with multidelay , 2002 .

[9]  Jinde Cao,et al.  Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification , 2007 .

[10]  Chi-Chuan Hwang,et al.  Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays , 2008 .

[11]  Zhongkui Sun,et al.  Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays , 2007 .

[12]  Xinzhi Liu,et al.  Impulsive synchronization of chaotic systems subject to time delay , 2009 .

[13]  Reggie Brown,et al.  APPROXIMATING THE MAPPING BETWEEN SYSTEMS EXHIBITING GENERALIZED SYNCHRONIZATION , 1998 .

[14]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  E. M. Shahverdiev,et al.  Chaos synchronization between the Mackey–Glass systems with multiple time delays , 2006 .

[16]  R. Femat,et al.  On the chaos synchronization phenomena , 1999 .

[17]  M. Sayed,et al.  Stability study and control of helicopter blade flapping vibrations , 2011 .