Exponential Stability of Fuzzy Cellular Neural Networks with Time-Varying Delays and Impulses

In this paper, a generalized model of fuzzy cellular neural networks (FCNNs) with time-varying delays and impulses is formulated and investigated. By employing the delay differential inequality with impulses initial conditions and the M-matrix theory, some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for FCNNs with time-varying delays and impulses are obtained. In particular, a more precise estimate of exponential convergence rate is provided. An example is given to show the effectiveness of the obtained results.

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

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

[3]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[4]  Daoyi Xu,et al.  Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays , 2006, Appl. Math. Comput..

[5]  Wansheng Tang,et al.  Exponential stability of fuzzy cellular neural networks with constant and time-varying delays , 2004 .

[6]  Qianhong Zhang,et al.  Global asymptotic stability of fuzzy cellular neural networks with time-varying delays , 2008 .

[7]  Tingwen Huang.  Exponential stability of fuzzy cellular neural networks with distributed delay , 2006 .

[8]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

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

[10]  Korris Fu-Lai Chung,et al.  Applying the improved fuzzy cellular neural network IFCNN to white blood cell detection , 2007, Neurocomputing.

[11]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

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

[13]  Jinde Cao.  A set of stability criteria for delayed cellular neural networks , 2001 .

[14]  S. Arik,et al.  Equilibrium analysis of delayed CNNs , 1998 .

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

[16]  Kelin Li,et al.  Stability of Cohen-Grossberg-type Fuzzy Cellular Neural Networks with Distributed Delays and Impulses , 2009, 2009 WRI Global Congress on Intelligent Systems.

[17]  Kelin Li,et al.  BEHAVIOR OF IMPULSIVE FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS , 2007 .

[18]  Kelin Li.  Stability analysis for impulsive Cohen–Grossberg neural networks with time-varying delays and distributed delays , 2009 .

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

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

[21]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[22]  Zhidong Teng,et al.  Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays , 2008, Neurocomputing.

[23]  Shitong Wang,et al.  Advanced fuzzy cellular neural network: Application to CT liver images , 2007, Artif. Intell. Medicine.

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

[25]  Q. Song,et al.  Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays , 2008 .

[26]  Jigen Peng,et al.  Delay-independent criteria for exponential stability of generalized Cohen-Grossberg neural networks with discrete delays , 2006 .

[27]  Jinde Cao,et al.  Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays , 2006, Neurocomputing.

[28]  Jinde Cao,et al.  Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses , 2008, J. Frankl. Inst..