Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components

The purpose of this paper is to investigate the problem of robust passivity analysis for delayed stochastic impulsive neural networks with leakage and additive time-varying delays. The novel contribution of this paper lies in the consideration of a new integral inequality proved to be well-known Jensen's inequality and takes fully the relationship between the terms in the Leibniz-Newton formula within the framework of linear matrix inequalities (LMIs). By constructing a suitable Lyapunov-Krasovskii functional with triple and four integral terms using Jensen's inequality, integral inequality technique and LMI frame work, which guarantees stability for the passivity of addressed neural networks. This LMI can be easily solved via convex optimization techniques. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

[1]  Shiguo Peng.  Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms , 2010 .

[2]  Yu Zhao,et al.  Asymptotic stability analysis of neural networks with successive time delay components , 2008, Neurocomputing.

[3]  Jun Li,et al.  Stability of uncertain impulsive stochastic fuzzy neural networks with two additive time delays in the leakage term , 2014, Neural Computing and Applications.

[4]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

[5]  Jinde Cao,et al.  Global exponential stability results for neutral-type impulsive neural networks , 2010 .

[6]  Ju H. Park,et al.  Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties , 2012 .

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

[8]  Huaguang Zhang,et al.  Improved Robust Stability Criteria for Delayed Cellular Neural Networks via the LMI Approach , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Qing-Long Han,et al.  On stabilization for systems with two additive time-varying input delays arising from networked control systems , 2012, J. Frankl. Inst..

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

[11]  Zhenjiang Zhao,et al.  Passivity analysis of stochastic neural networks with time-varying delays and leakage delay , 2014, Neurocomputing.

[12]  Qing-Long Han,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-Varying Delay Components , 2011, IEEE Transactions on Neural Networks.

[13]  R. Sakthivel,et al.  New exponential stability criteria for stochastic BAM neural networks with impulses , 2010 .

[14]  Goshaidas Ray,et al.  Stability analysis for continuous system with additive time-varying delays: A less conservative result , 2010, Appl. Math. Comput..

[15]  Huaguang Zhang,et al.  On passivity analysis for stochastic neural networks with interval time-varying delay , 2010, Neurocomputing.

[16]  Yajuan Liu,et al.  Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components , 2015, Neurocomputing.

[17]  Xiaofeng Liao,et al.  Passivity and Passification of Fuzzy Systems with Time Delays , 2006, Comput. Math. Appl..

[18]  Rajendran Samidurai,et al.  Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses , 2013, J. Frankl. Inst..

[19]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

[20]  Martin Bohner,et al.  An impulsive delay differential inequality and applications , 2012, Comput. Math. Appl..

[21]  James Lam,et al.  Corrigendum to "Stability analysis for continuous systems with two additive time-varying delay components": [Systems Control Lett. 56(2007) 16-24] , 2007, Syst. Control. Lett..

[22]  Jinde Cao,et al.  Passivity of uncertain neural networks with both leakage delay and time-varying delay , 2012 .

[23]  Yi Zhao,et al.  Global synchronization of nonlinear coupled complex dynamical networks with information exchanges at discrete-time , 2015, Neurocomputing.

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

[25]  Rajendran Samidurai,et al.  Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays , 2014, Neural Computing and Applications.

[26]  Xiaodi Li,et al.  LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays☆ , 2011 .

[27]  Wei Zhang,et al.  Robust stability analysis of uncertain systems with two additive time-varying delay components , 2009 .

[28]  Pagavathigounder Balasubramaniam,et al.  Global Robust Passivity Analysis for Stochastic Interval Neural Networks with Interval Time-Varying Delays and Markovian Jumping Parameters , 2011, J. Optim. Theory Appl..

[29]  Qiankun Song,et al.  Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations , 2012, J. Frankl. Inst..

[30]  Jinde Cao,et al.  Robust Stability of Markovian Jump Stochastic Neural Networks with Time Delays in the Leakage Terms , 2013, Neural Processing Letters.

[31]  R. Rakkiyappan,et al.  Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[32]  Yingmin Jia,et al.  New approaches on stability criteria for neural networks with two additive time-varying delay components , 2013, Neurocomputing.

[33]  Qiankun Song,et al.  Passivity analysis of discrete-time stochastic neural networks with time-varying delays , 2009, Neurocomputing.

[34]  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).

[35]  Min Wu,et al.  Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

[37]  K. Gopalsamy.  Leakage delays in BAM , 2007 .

[38]  R. Rakkiyappan,et al.  Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control , 2015, J. Frankl. Inst..

[39]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[41]  Jianwen Feng,et al.  Cluster synchronisation of non-linearly coupled Lur'e networks with identical and non-identical nodes and an asymmetrical coupling matrix , 2013 .

[42]  Pagavathigounder Balasubramaniam,et al.  Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays , 2011, Math. Comput. Model..

[43]  Pagavathigounder Balasubramaniam,et al.  Global Passivity Analysis of Interval Neural Networks with Discrete and Distributed Delays of Neutral Type , 2010, Neural Processing Letters.

[44]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[45]  Ju H. Park,et al.  Effects of leakage time-varying delays in Markovian jump neural networks with impulse control , 2013, Neurocomputing.

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

[47]  R. Lu,et al.  Passivity analysis of stochastic time-delay neural networks , 2010 .

[48]  R. Sakthivel,et al.  EXPONENTIAL STABILITY FOR STOCHASTIC NEURAL NETWORKS OF NEUTRAL TYPE WITH IMPULSIVE EFFECTS , 2010 .

[49]  Jinde Cao,et al.  Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term , 2014 .

[50]  Ju H. Park,et al.  Mean square exponential synchronization for impulsive coupled neural networks with time-varying delays and stochastic disturbances , 2016, Complex..

[51]  Pin-Lin Liu,et al.  Robust exponential stability for uncertain time-varying delay systems with delay dependence , 2009, J. Frankl. Inst..