Delay-Dependent Exponential Synchronization Criteria for Chaotic Neural Networks with Time-Varying Delays

The problem of exponentially synchronizing class of delayed neural networks is studied. Both constant and time-varying delays are considered, to obtain the delay-dependent state feedback synchronization gain matrix. By means of the method of Lyapunov–Krasovskii functional, combined with linear matrix inequalities, exponential synchronization of the master–slave structure of neural networks is achieved. The delay interval is decomposed into multiple nonequidistant subintervals, on which Lyapunov–Krasovskii functionals are constructed. On the basis of these functionals, a new exponential synchronization condition, one that is time-delay dependent, is proposed in terms of linear matrix inequalities. A numerical example showing the effectiveness of the proposed method is presented.

[1]  Qing-Long Han,et al.  Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays , 2011, IEEE Trans. Neural Networks.

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

[3]  Jinde Cao,et al.  An LMI approach to delay-dependent state estimation for delayed neural networks , 2008, Neurocomputing.

[4]  Q. Han,et al.  A delay decomposition approach to delay‐dependent stability for linear systems with time‐varying delays , 2009 .

[5]  Wei Ding,et al.  Synchronization schemes of a class of fuzzy cellular neural networks based on adaptive control , 2010 .

[6]  Jiming Hu,et al.  Synchronization conditions for chaotic nonlinear continuous neural networks , 2009 .

[7]  Xuyang Lou,et al.  Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control , 2009 .

[8]  Pagavathigounder Balasubramaniam,et al.  Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time-varying delay , 2011 .

[9]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[10]  Hongjie Yu,et al.  Chaotic synchronization based on stability criterion of linear systems , 2003 .

[11]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[13]  S. Jeeva Sathya Theesar,et al.  Synchronization of chaotic nonlinear continuous neural networks with time-varying delay , 2011, Cognitive Neurodynamics.

[14]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of neural networks with time-varying delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[16]  Xuyang Lou,et al.  New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, Neurocomputing.

[17]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[18]  Huaguang Zhang,et al.  New Delay-Dependent Global Exponential Stability Criterion for Cellular-Type Neural Networks With Time-Varying Delays , 2009, IEEE Trans. Circuits Syst. II Express Briefs.

[19]  Q. Han.  A delay decomposition approach to stability and H∞ control of linear time-delay systems — part I: Stability , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[20]  S. Zhong,et al.  Exponential synchronization of neural networks with time-varying delays , 2009 .

[21]  P. Balasubramaniam,et al.  State estimation for Markovian jumping recurrent neural networks with interval time-varying delays , 2010 .

[22]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[23]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.