Dissipativity analysis of stochastic neural networks with time delays

This paper is concerned with the dissipativity problem of stochastic neural networks with time delay. A new stochastic integral inequality is first proposed. By utilizing the delay partitioning technique combined with the stochastic integral inequalities, some sufficient conditions ensuring mean-square exponential stability and dissipativity are derived. Some special cases are also considered. All the given results in this paper are not only dependent upon the time delay, but also upon the number of delay partitions. Finally, some numerical examples are provided to illustrate the effectiveness and improvement of the proposed criteria.

[1]  Xuerong Mao,et al.  Exponential stability and instability of stochastic neural networks 1 , 1996 .

[2]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[3]  B. Brogliato,et al.  Dissipative Systems Analysis and Control , 2000 .

[4]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[5]  Madan M. Gupta,et al.  Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory , 2003 .

[6]  J. H. Park.  Design of a dynamic output feedback controller for a class of neutral systems with discrete and distributed delays , 2004 .

[7]  Daniel W. C. Ho,et al.  State estimation for delayed neural networks , 2005, IEEE Transactions on Neural Networks.

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

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

[10]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[11]  Dimitri Peaucelle,et al.  Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation , 2007, Autom..

[12]  Huijun Gao,et al.  Stability analysis for continuous systems with two additive time-varying delay components , 2007, Syst. Control. Lett..

[13]  Ju H. Park,et al.  LMI optimization approach on stability for delayed neural networks of neutral-type , 2008, Appl. Math. Comput..

[14]  James Lam,et al.  Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays , 2008, Int. J. Control.

[15]  Yurong Liu,et al.  State estimation for jumping recurrent neural networks with discrete and distributed delays , 2009, Neural Networks.

[16]  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).

[17]  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.

[18]  G. Duan,et al.  Improved L2–L∞ filtering for stochastic time-delay systems , 2010 .

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

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

[21]  C. Ahn.  Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks , 2010 .

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

[23]  Min Wu,et al.  Improved delay-dependent stability analysis for uncertain stochastic neural networks with time-varying delay , 2011, Neural Computing and Applications.

[24]  Wei Xing Zheng,et al.  Stability and $L_{2}$ Performance Analysis of Stochastic Delayed Neural Networks , 2011, IEEE Transactions on Neural Networks.

[25]  Bin Jiang,et al.  Fault detection for discrete-time switched systems with interval time-varying delays , 2011 .

[26]  Liguang Xu.  Exponential p-stability of singularly perturbed impulsive stochastic delay differential systems , 2011 .

[27]  James Lam,et al.  α-Dissipativity analysis of singular time-delay systems , 2011, Autom..

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

[29]  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..

[30]  James Lam,et al.  Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[31]  Tao Li,et al.  Exponential synchronization for arrays of coupled neural networks with time-delay couplings , 2011 .

[32]  Ju H. Park,et al.  New results on exponential passivity of neural networks with time-varying delays , 2012 .

[33]  K. C. Cheung,et al.  Passivity criteria for continuous-time neural networks with mixed time-varying delays , 2012, Appl. Math. Comput..

[34]  Huabin Chen,et al.  Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays , 2012 .

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

[36]  James Lam,et al.  Stability and Dissipativity Analysis of Static Neural Networks With Time Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Shouming Zhong,et al.  Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates , 2012, Appl. Math. Comput..

[38]  Zhengqiu Zhang,et al.  New global exponential stability result to a general Cohen–Grossberg neural networks with multiple delays , 2011, Nonlinear Dynamics.

[39]  Sabri Arik,et al.  Equilibrium and stability analysis of delayed neural networks under parameter uncertainties , 2012, Appl. Math. Comput..