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

In this paper, based on Lyapunov-Krasovskii functional approach and proper integral inequality, one novel sufficient condition is derived to guarantee the global stability for neural networks with interval time-varying delay, in which the general convex combination is employed. The LMI-based criterion heavily depends on the upper and lower bounds on both time delay and its derivative, which is different from those existent ones and has wider application fields than some present results. Finally, two numerical examples can illustrate the less conservatism of the proposed methods.

[1]  Wei Xing Zheng,et al.  Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Wei Xing Zheng,et al.  Improved Delay-Dependent Asymptotic Stability Criteria for Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[3]  Qing-Long Han,et al.  On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

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

[6]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .

[7]  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.

[8]  Dong Yue,et al.  New stability criteria of neural networks with interval time-varying delay: A piecewise delay method , 2009, Appl. Math. Comput..

[9]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

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

[11]  Qing Zhu,et al.  New results of global robust exponential stability of neural networks with delays , 2010 .

[12]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[13]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[14]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[15]  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).

[16]  R. Rakkiyappan,et al.  Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays , 2009 .

[17]  Vimal Singh,et al.  Global robust stability of delayed neural networks: an LMI approach , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[19]  Krishnan Balachandran,et al.  Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays , 2010 .

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

[21]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.

[22]  Jinde Cao,et al.  Global exponential stability and periodicity of recurrent neural networks with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Shengyuan Xu,et al.  On Equivalence and Efficiency of Certain Stability Criteria for Time-Delay Systems , 2007, IEEE Transactions on Automatic Control.

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

[25]  Huaguang Zhang,et al.  New Delay-Dependent Global Exponential Stability Criterion for Cellular-Type Neural Networks With Time-Varying Delays , 2009, IEEE Trans. Circuits Syst. II Express Briefs.

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

[27]  Huaguang Zhang,et al.  Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay , 2009, Neurocomputing.

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

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

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

[31]  P. Balasubramaniam,et al.  Delay-range dependent stability criteria for neural networks with Markovian jumping parameters , 2009 .

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

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

[34]  Qiang Zhang,et al.  Global exponential stability for nonautonomous cellular neural networks with delays , 2006 .

[35]  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).

[36]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

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

[38]  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.

[39]  Dong Yue,et al.  Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  J. Lam,et al.  Novel global robust stability criteria for interval neural networks with multiple time-varying delays , 2005 .

[41]  Pagavathigounder Balasubramaniam,et al.  Stability analysis of uncertain fuzzy Hopfield neural networks with time delays , 2009 .

[42]  Pagavathigounder Balasubramaniam,et al.  Exponential stability of uncertain stochastic fuzzy BAM neural networks with time-varying delays , 2009, Neurocomputing.

[43]  Hanyong Shao,et al.  New delay-dependent stability criteria for systems with interval delay , 2009, Autom..