Output feedback ℋ∞ synchronization for delayed chaotic neural networks

In this paper, we propose a new output feedback ℋ∞ synchronization method for delayed chaotic neural networks with external disturbance. Based on Lyapunov–Krasovskii theory and linear matrix inequality (LMI) approach, the output feedback ℋ∞ synchronization controller is presented to not only guarantee stable synchronization, but also reduce the effect of external disturbance to an ℋ∞ norm constraint. The proposed controller can be obtained by solving the LMI problem. An illustrative example is given to demonstrate the effectiveness of the proposed method.

[1]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[2]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[3]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[4]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

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

[6]  Jinde Cao,et al.  Stability and Hopf Bifurcation in a Simplified BAM Neural Network With Two Time Delays , 2007, IEEE Transactions on Neural Networks.

[7]  Anton A. Stoorvogel,et al.  The H ∞ control problem: a state space approach , 2000 .

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

[9]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[10]  Jun-Guo Lu,et al.  Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach , 2009 .

[11]  Ju H. Park,et al.  H∞ synchronization of chaotic systems via dynamic feedback approach , 2008 .

[12]  Jinde Cao,et al.  Exponential synchronization of stochastic perturbed chaotic delayed neural networks , 2007, Neurocomputing.

[13]  M. Gilli.  Strange attractors in delayed cellular neural networks , 1993 .

[14]  Yan Huang,et al.  A New Class of Chaotic Simple Three-Neuron Cellular Neural Networks , 2006, Int. J. Bifurc. Chaos.

[15]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of chaotic neural networks , 2005 .

[16]  T. Liao,et al.  H∞ synchronization of chaotic systems using output feedback control design , 2007 .

[17]  A. Das,et al.  Chaos in a Three-Dimensional General Model of Neural Network , 2002, Int. J. Bifurc. Chaos.

[18]  Zhigang Zeng,et al.  Improved conditions for global exponential stability of recurrent neural networks with time-varying delays , 2006, IEEE Transactions on Neural Networks.

[19]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[20]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[21]  Jinde Cao,et al.  Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects , 2007 .

[22]  L. Ghaoui,et al.  History of linear matrix inequalities in control theory , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[23]  Jinde Cao,et al.  Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters , 2008 .

[24]  Erik Noldus,et al.  Stabilization of a class of distributional convolution equations , 1985 .