Reliable synchronization of nonlinear chaotic systems

This article addresses the reliable synchronization problem for a general class of chaotic systems. By combining the Lyapunov stability theory with the linear matrix inequality (LMI) optimization technique, a reliable feedback controller is established to guarantee synchronization between the master and slave chaotic systems even though some control component (actuator) failures occur. Finally, an illustrative example is provided to demonstrate the effectiveness of the results developed in this paper.

[1]  P. Das,et al.  Chaos in an effective four-neuron neural network , 1991 .

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

[3]  H. Yau.  Design of adaptive sliding mode controller for chaos synchronization with uncertainties , 2004 .

[4]  José Manoel Balthazar,et al.  On an optimal control design for Rössler system , 2004 .

[5]  Huai-Ning Wu,et al.  Reliable$rm H_infty $Fuzzy Control for Continuous-Time Nonlinear Systems With Actuator Failures , 2006, IEEE Transactions on Fuzzy Systems.

[6]  Wen Yu.  Passive equivalence of chaos in Lorenz system , 1999 .

[7]  Jitao Sun,et al.  Impulsive control and synchronization of Chua's oscillators , 2004, Math. Comput. Simul..

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

[9]  Jitao Sun,et al.  Controlling chaotic Lu systems using impulsive control , 2005 .

[10]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

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

[12]  Dragoslav D. Siljak,et al.  Control of large-scale systems: Beyond decentralized feedback , 2004, Annu. Rev. Control..

[13]  Jinde Cao,et al.  Cryptography based on delayed chaotic neural networks , 2006 .

[14]  Wang Fu-zhong,et al.  LMI approach to reliable H ∞ control of linear systems , 2006 .

[15]  F. M. Moukam Kakmeni,et al.  Chaos synchronization and duration time of a class of uncertain chaotic systems , 2006, Math. Comput. Simul..

[16]  Li Yu,et al.  An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure , 2005, Appl. Math. Comput..

[17]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[18]  Jingcheng Wang,et al.  Delay-dependent robust and reliable H∞ control for uncertain time-delay systems with actuator failures , 2000, J. Frankl. Inst..

[19]  Xiao-Song Yang,et al.  Chaos and transient chaos in simple Hopfield neural networks , 2005, Neurocomputing.

[20]  Y. Ohta,et al.  Parametric Absolute Stability of Lur'e Systems , 1994 .

[21]  Heinz Unbehauen,et al.  Robust reliable control for a class of uncertain nonlinear state-delayed systems , 1999, Autom..

[22]  Her-Terng Yau,et al.  Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems , 2006 .

[23]  Jinde Cao,et al.  Adaptive exponential synchronization of delayed chaotic networks , 2006 .

[24]  D. Siljak,et al.  Robust stabilization of nonlinear systems: The LMI approach , 2000 .

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

[26]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .