Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays

This paper is concerned with the problem of delay-dependent stability criteria for recurrent neural networks with time-varying delays. A new class of Lyapunov functional is introduced by decomposing the delays in all integral terms. By exploiting all possible information in various delay intervals and using reciprocally convex approach, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived results.

[1]  Tao Li,et al.  Improved stability criteria of neural networks with time-varying delays: An augmented LKF approach , 2010, Neurocomputing.

[2]  Huijun Gao,et al.  New Delay-Dependent Exponential Stability for Neural Networks With Time Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Tao Li,et al.  Further Results on Delay-Dependent Stability Criteria of Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

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

[5]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[6]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[7]  Ju H. Park,et al.  Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates , 2012 .

[8]  Xun-lin Zhu,et al.  Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays , 2009 .

[9]  Zhi-Hong Guan,et al.  Delay-dependent exponential stability of neural networks with variable delays , 2004 .

[10]  X. Guan,et al.  New results on stability analysis of neural networks with time-varying delays , 2006 .

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

[12]  Ju H. Park,et al.  Passivity-based control for Hopfield neural networks using convex representation , 2011, Appl. Math. Comput..

[13]  C. Scherer,et al.  Linear Matrix Inequalities in Control , 2011 .

[14]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[15]  Jinde Cao,et al.  New conditions for global exponential stability of cellular neural networks with delays , 2005, Neural Networks.

[16]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Wei Xing Zheng,et al.  Delay-Slope-Dependent Stability Results of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.

[18]  S. Arik.  Global asymptotic stability of a larger class of neural networks with constant time delay , 2003 .

[19]  Yu Zhao,et al.  Further improvement on synchronization stability of complex networks with coupling delays , 2008, Int. J. Comput. Math..

[20]  Ju H. Park,et al.  Further results on state estimation for neural networks of neutral-type with time-varying delay , 2009, Appl. Math. Comput..

[21]  James Lam,et al.  A New Criterion of Delay-Dependent Asymptotic Stability for Hopfield Neural Networks With Time Delay , 2008, IEEE Transactions on Neural Networks.

[22]  LiaoXiaofeng,et al.  Delay-dependent exponential stability analysis of delayed neural networks , 2002 .

[23]  Pagavathigounder Balasubramaniam,et al.  Design of state estimator for neural networks with leakage, discrete and distributed delays , 2012, Appl. Math. Comput..

[24]  Ju H. Park,et al.  A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays , 2011, Appl. Math. Comput..

[25]  Shouming Zhong,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components , 2012 .

[26]  Huijun Gao,et al.  New Passivity Analysis for Neural Networks With Discrete and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[27]  Yong He,et al.  Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

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

[29]  Wei Xing Zheng,et al.  Delay-Dependent Exponential Stability of Neural Networks With Variable Delay: An LMI Approach , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Xiangjun Xie,et al.  New asymptotic stability criteria for neural networks with time-varying delay , 2010 .

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

[32]  Shen-Ping Xiao,et al.  New Globally Asymptotic Stability Criteria for Delayed Cellular Neural Networks , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[33]  Z. Guan,et al.  An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay , 2005, TENCON 2005 - 2005 IEEE Region 10 Conference.

[34]  Dong Yue,et al.  Delay-Distribution-Dependent Exponential Stability Criteria for Discrete-Time Recurrent Neural Networks With Stochastic Delay , 2008, IEEE Transactions on Neural Networks.

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

[36]  Jian Sun,et al.  Improved stability criteria for neural networks with time-varying delay , 2009 .

[37]  Zhanshan Wang,et al.  New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks , 2009, Neurocomputing.

[38]  Ju H. Park,et al.  Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data , 2012 .

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

[40]  Ju H. Park,et al.  IMPROVED RESULTS ON STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS: NOVEL DELAY-DEPENDENT CRITERIA , 2010 .

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

[42]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[45]  Shengyuan Xu,et al.  A new approach to exponential stability analysis of neural networks with time-varying delays , 2006, Neural Networks.

[46]  Ju H. Park,et al.  Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays , 2010 .

[47]  Ju H. Park,et al.  A novel delay-dependent criterion for delayed neural networks of neutral type , 2010 .

[48]  P. Shi,et al.  New stability criteria for Cohen-Grossberg neural networks with time delays , 2009 .