An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

[1]  Zhang Yi,et al.  Continuous attractors of a class of recurrent neural networks without lateral inhibition , 2008, 2008 IEEE Conference on Cybernetics and Intelligent Systems.

[2]  Xuyang Lou,et al.  Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[3]  H. B. Huang,et al.  Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty , 2005 .

[4]  Ligang Wu,et al.  Exponential stabilization of switched stochastic dynamical networks , 2009 .

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

[6]  Leon O. Chua,et al.  Detecting simple motion using cellular neural networks , 1990, IEEE International Workshop on Cellular Neural Networks and their Applications.

[7]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

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

[9]  Jinde Cao,et al.  Cluster synchronization in an array of hybrid coupled neural networks with delay , 2009, Neural Networks.

[10]  Zhidong Teng,et al.  Global eponential stability of cellular neural networks with time-varying coefficients and delays , 2004, Neural Networks.

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

[12]  Daoyi Xu,et al.  Global attraction and stability for Cohen-Grossberg neural networks with delays , 2006, Neural Networks.

[13]  Jinde Cao,et al.  Multistability and multiperiodicity of delayed Cohen–Grossberg neural networks with a general class of activation functions , 2008 .

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

[15]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[16]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[17]  Leon O. Chua,et al.  Cellular neural networks with non-linear and delay-type template elements and non-uniform grids , 1992, Int. J. Circuit Theory Appl..

[18]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[19]  D. Xie,et al.  Average dwell-time approach to L2 gain control synthesis of switched linear systems with time delay in detection of switching signal , 2009 .

[20]  Jinde Cao,et al.  Convergence Dynamics of Stochastic Cohen–Grossberg Neural Networks With Unbounded Distributed Delays , 2011, IEEE Transactions on Neural Networks.

[21]  Wen-an Zhang,et al.  Stability analysis for discrete-time switched time-delay systems , 2009, Autom..

[22]  Jinde Cao,et al.  Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure , 2007 .

[23]  Jun Zhao,et al.  Synchronization of Complex Dynamical Networks with Switching Topology: a Switched System Point of View , 2008 .

[24]  Kai Zhang,et al.  Exponential stability for switched Cohen–Grossberg neural networks with average dwell time , 2011, Proceedings of the 29th Chinese Control Conference.

[25]  Jinde Cao,et al.  Synchronization control of switched linearly coupled neural networks with delay , 2010, Neurocomputing.