New delay-dependent stability criteria for uncertain stochastic neural networks with discrete interval and distributed delays

This paper studies the globally robustly asymptotical stability in mean square of uncertain stochastic neural networks with discrete interval and distributed time-varying delays. By constructing an augmented Lyapunov-Krasovskii functional, some delay-dependent criteria for the globally robustly asymptotical stability of such systems are formulated in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the obtained results.

[1]  Yonggang Chen,et al.  Mean square exponential stability of uncertain stochastic neural networks with time-varying delay , 2009, Neurocomputing.

[2]  Xinzhi Liu,et al.  Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays , 2011, Neurocomputing.

[3]  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.

[4]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[5]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[6]  Xinzhi Liu,et al.  New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays , 2010, Neural Processing Letters.

[7]  Zidong Wang,et al.  Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays , 2008 .

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

[9]  Feipeng Da,et al.  Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays , 2009 .

[10]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Ju H. Park,et al.  Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays , 2008, Appl. Math. Comput..

[12]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

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

[14]  Shigeng Hu,et al.  Stability analysis of stochastic recurrent neural networks with unbounded time-varying delays , 2011, Neurocomputing.

[15]  Kanjian Zhang,et al.  Further results on mean square exponential stability of uncertain stochastic delayed neural networks , 2009 .

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

[17]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Peng Hu,et al.  Further results on delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays and Markovian jump parameters , 2012, Neural Computing and Applications.

[19]  Xiangbing Zhou,et al.  Improved asymptotic stability criteria for neural networks with interval time-varying delay , 2010, Expert Syst. Appl..

[20]  Peng Shi,et al.  A new criterion for exponential stability of uncertain stochastic neural networks with mixed delays , 2008, Math. Comput. Model..

[21]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays , 2009, Neurocomputing.

[22]  Shouming Zhong,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delay , 2011, Appl. Math. Comput..

[23]  Pagavathigounder Balasubramaniam,et al.  Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties , 2009, Neurocomputing.

[24]  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).

[25]  G. Feng,et al.  Delay-dependent stability for uncertain stochastic neural networks with time-varying delay , 2007 .

[26]  Sabri Arik,et al.  Global Robust Stability of Bidirectional Associative Memory Neural Networks With Multiple Time Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[28]  Changyin Sun,et al.  Improved delay-dependent stability criteria for neural networks with time-varying delay , 2008, WCICA 2008.

[29]  Lei Liu,et al.  Exponential Stability of Uncertain Stochastic Neural Networks with Markovian Switching , 2010, Neural Processing Letters.

[30]  Hongyi Li,et al.  Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays☆ , 2008 .

[31]  Shengyuan Xu,et al.  New results on global exponential stability of recurrent neural networks with time-varying delays , 2006 .

[32]  Kaiyu Liu,et al.  An improved global exponential stability criterion for delayed neural networks , 2009 .

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

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

[35]  Peng Hu,et al.  Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks , 2010, Neurocomputing.

[36]  Pagavathigounder Balasubramaniam,et al.  Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays , 2008 .

[37]  Jinde Cao,et al.  Stability analysis of delayed cellular neural networks , 1998, Neural Networks.

[38]  James Lam,et al.  Robust Stability for Interval Stochastic Neural Networks with Time-Varying Discrete and Distributed Delays , 2011 .

[39]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

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

[41]  Ruya Samli,et al.  New results for global stability of a class of neutral-type neural systems with time delays , 2009, Appl. Math. Comput..

[42]  Jinde Cao,et al.  pth moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching , 2011, Nonlinear Dynamics.

[43]  Sheng Zhou,et al.  Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays , 2009, Neural Processing Letters.

[44]  Jinde Cao,et al.  Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters , 2009 .

[45]  Wu‐Hua Chen,et al.  Mean square exponential stability of uncertain stochastic delayed neural networks , 2008 .

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

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

[48]  Jian Sun,et al.  New delay-dependent stability criteria for neural networks with time-varying interval delay ✩ , 2010 .

[49]  James Lam,et al.  Global exponential estimates of stochastic interval neural networks with discrete and distributed delays , 2008, Neurocomputing.

[50]  Yaonan Wang,et al.  Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays , 2010, Neurocomputing.

[51]  Shengyuan Xu,et al.  Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.