-Stability of Impulsive Neural Networks with Unbounded Time-Varying Delays and Continuously Distributed Delays

This paper is concerned with the problem of -stability of impulsive neural systems with unbounded time-varying delays and continuously distributed delays. Some -stability criteria are derived by using the Lyapunov-Krasovskii functional method. Those criteria are expressed in the form of linear matrix inequalities (LMIs), and they can easily be checked. A numerical example is provided to demonstrate the effectiveness of the obtained results.

[1]  Rathinasamy Sakthivel,et al.  Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects , 2010 .

[2]  Qiang Zhang,et al.  Delay-dependent global stability results for delayed Hopfield neural networks , 2007 .

[3]  Xinzhi Liu,et al.  Exponential stability of impulsive cellular neural networks with time delay via Lyapunov functionals , 2007, Appl. Math. Comput..

[4]  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.

[5]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[7]  Tianping Chen,et al.  Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays , 2008 .

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

[9]  Vimal Singh,et al.  On global robust stability of interval Hopfield neural networks with delay , 2007 .

[10]  Tianping Chen,et al.  Global $\mu$ -Stability of Delayed Neural Networks With Unbounded Time-Varying Delays , 2007, IEEE Transactions on Neural Networks.

[11]  Ou Ou,et al.  Global robust exponential stability of delayed neural networks: An LMI approach , 2007 .

[12]  J. Kato.  Stability in functional differential equations , 1980 .

[13]  Yu Zhang,et al.  Stability of impulsive neural networks with time delays , 2005 .

[14]  Chuandong Li,et al.  An LMI approach to asymptotical stability of multi-delayed neural networks , 2005 .

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

[16]  Xiaodi Li.  Uniform asymptotic stability and global stability of impulsive infinite delay differential equations , 2009 .

[17]  Pagavathigounder Balasubramaniam,et al.  On exponential stability results for fuzzy impulsive neural networks , 2010, Fuzzy Sets Syst..

[18]  Rajendran Samidurai,et al.  Asymptotic Stability of Stochastic Delayed Recurrent Neural Networks with Impulsive Effects , 2010, J. Optim. Theory Appl..

[19]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[20]  Jinde Cao,et al.  Global exponential stability results for neutral-type impulsive neural networks , 2010 .

[21]  K. Gopalsamy,et al.  Exponential stability of artificial neural networks with distributed delays and large impulses , 2008 .

[22]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

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

[24]  S. Mohamad,et al.  Exponential stability in Hopfield-type neural networks with impulses , 2007 .

[25]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

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

[27]  R. Sakthivel,et al.  New exponential stability criteria for stochastic BAM neural networks with impulses , 2010 .

[28]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[29]  Xiaoshu Luo,et al.  Exponential stability of impulsive neural networks with time-varying delays , 2008 .

[30]  S. Arik.  Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays , 2006 .

[31]  R. Rakkiyappan,et al.  Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations , 2010 .