Globally Exponential Stability of Impulsive Neural Networks with Given Convergence Rate

This paper deals with the stability problem for a class of impulsive neural networks. Some sufficient conditions which can guarantee the globally exponential stability of the addressed models with given convergence rate are derived by using Lyapunov function and impulsive analysis techniques. Finally, an example is given to show the effectiveness of the obtained results.

[1]  W. Marsden.  I and J , 2012 .

[2]  Martin Bohner,et al.  Exponential synchronization of chaotic neural networks with mixed delays and impulsive effects via output coupling with delay feedback , 2010, Math. Comput. Model..

[3]  Xinzhi Liu,et al.  Stability of impulsive control systems with time delay , 2004 .

[4]  Benedetta Lisena,et al.  Exponential stability of Hopfield neural networks with impulses , 2011 .

[5]  Xiaodi Li,et al.  Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays , 2009, Journal of Computational and Applied Mathematics.

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

[7]  H. Akça,et al.  Continuous-time additive Hopfield-type neural networks with impulses , 2004 .

[8]  Ivanka M. Stamova,et al.  Stability Analysis of Impulsive Functional Differential Equations , 2009 .

[9]  Jianhua Shen,et al.  Asymptotic behavior of solutions of nonlinear neutral differential equations with impulses , 2007 .

[10]  Jinde Cao,et al.  Global stability analysis in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Chuandong Li,et al.  Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: A Razumikhin approach , 2012, Neurocomputing.

[12]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems , 1996, Springer US.

[13]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

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

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

[16]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[17]  Xiaodi Li,et al.  Stability properties for Hopfield neural networks with delays and impulsive perturbations , 2009 .

[18]  Daoyi Xu,et al.  Stability Analysis of Delay Neural Networks With Impulsive Effects , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[19]  Ivanka M. Stamova,et al.  Global exponential stability for impulsive cellular neural networks with time-varying delays , 2008 .

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

[21]  Krishnan Balachandran,et al.  Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays , 2010 .

[22]  Xiaodi Li,et al.  New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays , 2010 .

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

[24]  Xinzhi Liu,et al.  The method of Lyapunov functionals and exponential stability of impulsive systems with time delay , 2007 .