On synchronization criterion for coupled discrete-time neural networks with interval time-varying delays

The purpose of this paper is to investigate the delay-dependent synchronization analysis for coupled discrete-time neural networks with interval time-varying delays in network couplings. Based on Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by construction of a suitable Lyapunov-Krasovskii's functional and utilization of Finsler's lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed method.

[1]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[3]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[4]  Guang-Hong Yang,et al.  Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay , 2008, 2008 American Control Conference.

[5]  Dong Yue,et al.  Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays , 2010, Neurocomputing.

[6]  Sabri Arik,et al.  New results for robust stability of dynamical neural networks with discrete time delays , 2010, Expert Syst. Appl..

[7]  S. Strogatz Exploring complex networks , 2001, Nature.

[8]  Qiankun Song,et al.  Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays , 2011, Neurocomputing.

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

[10]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

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

[12]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[13]  Sabri Arik,et al.  Equilibrium and stability analysis of delayed neural networks under parameter uncertainties , 2012, Appl. Math. Comput..

[14]  Jinde Cao,et al.  Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Hongye Su,et al.  New results on robust exponential stability for discrete recurrent neural networks with time-varying delays , 2009, Neurocomputing.

[16]  Yun Zou,et al.  Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays , 2008, Neurocomputing.

[17]  Tianping Chen,et al.  Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix , 2008 .

[18]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[19]  Tao Li,et al.  Exponential synchronization for arrays of coupled neural networks with time-delay couplings , 2011 .

[20]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[21]  Sabri Arik,et al.  Further analysis of global robust stability of neural networks with multiple time delays , 2012, J. Frankl. Inst..

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

[23]  Neyir Ozcan,et al.  A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays , 2009 .