LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations

Without assuming that the neuron activations are bounded, some delay-independent criteria for interval delayed neural networks with discontinuous neuron activations are derived to guarantee global robust stability by using the generalized Lyapunov method and linear matrix inequality (LMI) technique. The obtained results improve and extend those given in earlier literature, and two numerical examples are also given to show the effectiveness of our results.

[1]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[2]  Lihong Huang,et al.  Further results on the stability of delayed cellular neural networks , 2003 .

[3]  Ju H. Park Robust stability of bidirectional associative memory neural networks with time delays , 2006 .

[4]  Lihong Huang,et al.  Global robust stability of delayed neural networks with discontinuous activation functions , 2008 .

[5]  K. Deimling Fixed Point Theory , 2008 .

[6]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[7]  Jinde Cao,et al.  Robust Stability in Cohen–Grossberg Neural Network with both Time-Varying and Distributed Delays , 2008, Neural Processing Letters.

[8]  J. Hale Theory of Functional Differential Equations , 1977 .

[9]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[11]  S. Arik Global robust stability analysis of neural networks with discrete time delays , 2005 .

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

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

[14]  Shouchuan Hu Differential equations with discontinuous right-hand sides☆ , 1991 .

[15]  Jinde Cao,et al.  Global robust stability of interval neural networks with multiple time-varying delays , 2007, Math. Comput. Simul..

[16]  S. Arik,et al.  An analysis of global robust stability of neural networks with discrete time delays , 2006 .

[17]  Huiyan Zhu,et al.  Global stability of cellular neural networks with constant and variable delays , 2003 .

[18]  S. Arik Stability analysis of delayed neural networks , 2000 .

[19]  Xuyang Lou,et al.  On the global robust asymptotic stability of BAM neural networks with time-varying delays , 2006, Neurocomputing.

[20]  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.

[21]  Ju H. Park,et al.  Further note on global exponential stability of uncertain cellular neural networks with variable delays , 2007, Appl. Math. Comput..

[22]  J. Aubin,et al.  Existence of Solutions to Differential Inclusions , 1984 .

[23]  Vimal Singh,et al.  Novel LMI condition for global robust stability of delayed neural networks , 2007 .

[24]  Jun Wang,et al.  Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays , 2003 .

[25]  Hongtao Lu,et al.  On stability of nonlinear continuous-time neural networks with delays , 2000, Neural Networks.

[26]  Zengyun Wang,et al.  Robust Stability Criterion for Delayed Neural Networks with Discontinuous Activation Functions , 2009, Neural Processing Letters.

[27]  J. Lam,et al.  Global robust exponential stability analysis for interval recurrent neural networks , 2004 .