LMI approach to the global robust stability of a larger class of neural networks with delay

Sufficient conditions in the form of linear matrix inequality for the uniqueness and global asymptotic stability of the equilibrium point of a large class of uncertain neural networks with delay are presented. The conditions are based on norm-bounded uncertainties. An example is given to show the effectiveness of the obtained results. A comparison is made between the present approach and an earlier approach due to Lu, Rong and Chen. An error is corrected in an earlier publication.

[1]  Jinde Cao,et al.  Global robust stability of interval cellular neural networks with time-varying delays , 2005 .

[2]  Jinde Cao,et al.  New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays , 2007 .

[3]  S. Zhong,et al.  Exponential stability analysis of stochastic delayed cellular neural network , 2006 .

[4]  Vimal Singh,et al.  Robust stability of 2-D digital filters employing saturation , 2005, IEEE Signal Processing Letters.

[5]  Vimal Singh,et al.  Robust stability of 2-D discrete systems described by the Fornasini-Marchesini second model employing quantization/overflow nonlinearities , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  J. Lam,et al.  Novel global robust stability criteria for interval neural networks with multiple time-varying delays , 2005 .

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

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

[9]  Vimal Singh,et al.  A novel global robust stability criterion for neural networks with delay , 2005 .

[10]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

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

[12]  Zhidong Teng,et al.  Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays , 2006 .

[13]  Qiang Zhang,et al.  Stability analysis for cellular neural networks with variable delays , 2006 .

[14]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[15]  Qiang Zhang,et al.  Stability of delayed cellular neural networks , 2007 .

[16]  Li Wang,et al.  Globally exponential stability and periodic solutions of CNNS with variable coefficients and variable delays , 2006 .

[17]  Jigen Peng,et al.  A new stability criterion for discrete-time neural networks: Nonlinear spectral radius , 2007 .

[18]  Jinde Cao,et al.  A based-on LMI stability criterion for delayed recurrent neural networks , 2006 .

[19]  X. Lou,et al.  Global asymptotic stability of delay BAM neural networks with impulses , 2006 .

[20]  Qiang Zhang,et al.  Delay-dependent exponential stability of cellular neural networks with time-varying delays , 2005 .

[21]  Shengyuan Xu,et al.  Global asymptotic stability analysis for cellular neural networks with time delays , 2006 .

[22]  Vimal Singh,et al.  Global robust stability of delayed neural networks: an LMI approach , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .

[24]  K. Galkowski,et al.  Positive real control for uncertain two-dimensional systems , 2002 .

[25]  Yurong Liu,et al.  Global asymptotic stability of generalized bi-directional associative memory networks with discrete and distributed delays , 2006 .

[26]  V. Singh Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[27]  Y. Hung,et al.  Robust mixed H/sub 2//H/sub /spl infin// filtering with regional pole assignment for uncertain discrete-time systems , 2002 .

[28]  Wenli Zhu,et al.  Stability analysis of stochastic delayed cellular neural networks by LMI approach , 2006 .

[29]  Jinde Cao,et al.  Global robust stability of delayed recurrent neural networks , 2004 .

[30]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .

[31]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

[32]  Jinde Cao,et al.  A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach , 2005 .

[33]  Zidong Wang,et al.  Exponential stability of uncertain stochastic neural networks with mixed time-delays , 2007 .

[34]  Vimal Singh,et al.  Improved global robust stability criterion for delayed neural networks , 2007 .

[35]  Vimal Singh,et al.  A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks , 2004, IEEE Transactions on Neural Networks.

[36]  V. Singh,et al.  Global asymptotic stability of cellular neural networks with unequal delays: LMI approach , 2004 .

[37]  Tianguang Chu,et al.  Exponential stability of neural networks with variable delays via LMI approach , 2006 .

[38]  Vimal Singh,et al.  New global robust stability results for delayed cellular neural networks based on norm-bounded uncertainties , 2006 .

[39]  W. Zheng,et al.  Global robust stability for delayed neural networks with polytopic type uncertainties , 2005 .

[40]  Jinde Cao,et al.  Globally exponentially robust stability and periodicity of delayed neural networks , 2004 .

[41]  Tianping Chen,et al.  Global Convergence of Delayed Neural Network Systems , 2003, Int. J. Neural Syst..

[42]  Wei Zhang,et al.  Delay-dependent asymptotic stability of a two-neuron system with different time delays , 2006 .

[43]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .

[44]  Vimal Singh,et al.  Simplified LMI condition for global asymptotic stability of delayed neural networks , 2006 .

[45]  Tingwen Huang Exponential stability of delayed fuzzy cellular neural networks with diffusion , 2007 .