Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay

Abstract In this paper, the robust global exponential stability is investigated for the discrete-time recurrent neural networks (RNNs) with time-varying interval delay. By choosing an augmented Lyapunov–Krasovskii functional, delay-dependent results guaranteeing the global exponential stability and the robust exponential stability of the concerned neural network are obtained. The results are shown to be a generalization of some previous results, and less conservative than the existing works. Two numerical examples are given to demonstrate the applicability of the proposed method.

[1]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[2]  Changyin Sun,et al.  Exponential stability of recurrent neural networks with time-varying discrete and distributed delays , 2009 .

[3]  Jinde Cao Global stability conditions for delayed CNNs , 2001 .

[4]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.

[5]  Jinde Cao,et al.  Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  K. Gopalsamy,et al.  Exponential stability of continuous-time and discrete-time cellular neural networks with delays , 2003, Appl. Math. Comput..

[7]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[8]  Wu-Hua Chen,et al.  Global exponential stability for discrete-time neural networks with variable delays , 2006 .

[9]  Jinde Cao,et al.  Discrete-time bidirectional associative memory neural networks with variable delays , 2005 .

[10]  Min Wu,et al.  LMI-based stability criteria for neural networks with multiple time-varying delays , 2005 .

[11]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[12]  Meiqin Liu,et al.  Global asymptotic stability analysis of discrete-time Cohen–Grossberg neural networks based on interval systems , 2008 .

[13]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[14]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Ju H. Park,et al.  Novel delay-dependent robust stability criterion of delayed cellular neural networks , 2007 .

[16]  Zidong Wang,et al.  Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis , 2007 .

[17]  Tao Li,et al.  Further result on asymptotic stability criterion of neural networks with time-varying delays , 2007, Neurocomputing.

[18]  Shengyuan Xu,et al.  On global exponential stability of high-order neural networks with time-varying delays☆ , 2007 .

[19]  Ju H. Park Robust stability of bidirectional associative memory neural networks with time delays , 2006 .

[20]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[21]  Changyin Sun,et al.  New results on global asymptotic stability analysis for neural networks with time-varying delays , 2009 .

[22]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[23]  Lei Wang,et al.  Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay , 2008 .

[24]  Shengyuan Xu,et al.  Improved global robust asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Ralph R. Martin,et al.  Discrete-time BAM neural networks with variable delays , 2007 .

[26]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[27]  E. Zerrad,et al.  Quantum hypervirial theorems , 2006 .

[28]  Tao Li,et al.  Robust stability for neural networks with time-varying delays and linear fractional uncertainties , 2007, Neurocomputing.

[29]  S. Arik Global asymptotic stability of a class of dynamical neural networks , 2000 .

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

[31]  Jun Wang,et al.  Absolute exponential stability of a class of continuous-time recurrent neural networks , 2003, IEEE Trans. Neural Networks.

[32]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

[33]  Sabri Arik,et al.  Global stability analysis of neural networks with multiple time varying delays , 2005, IEEE Transactions on Automatic Control.

[34]  Shengyuan Xu,et al.  Delay-Dependent Robust Exponential Stability for Uncertain Recurrent Neural Networks with Time-Varying Delays , 2007, Int. J. Neural Syst..

[35]  Shumin Fei,et al.  Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays , 2008, Neurocomputing.

[36]  Zidong Wang,et al.  Robust stability of discrete-time stochastic neural networks with time-varying delays , 2008, Neurocomputing.

[37]  S. Arik Stability analysis of delayed neural networks , 2000 .

[38]  Lei Wang,et al.  Stability and bifurcation for discrete-time Cohen-Grossberg neural network , 2006, Appl. Math. Comput..

[39]  Shengyuan Xu,et al.  Novel global asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[40]  Jinde Cao,et al.  Global robust stability of interval neural networks with multiple time-varying delays , 2007, Math. Comput. Simul..

[41]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..