Stochastic synchronization of neural networks with multiple time-varying delays and Markovian jump

Abstract This paper addresses the stochastic synchronization problem for a class of neural networks with multiple time-varying delays and Markovian jump. By choosing a non-negative function, M-matrix technique and stochastic analysis approach, several sufficient conditions are obtained to guarantee that the error system is stable. Moreover, the update laws of the gain matrix are derived to ensure stochastic synchronization for multiple time-varying delayed drive system and response system. In particular, the M-matrix associates with the Markovian chain generated by transmission rate matrix. And the condition of M-matrix can be verified conveniently in practice. In the end, the effectiveness and potential value of the results addressed are tested by a simulation example.

[1]  Qiankun Song,et al.  Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling , 2010, Appl. Math. Comput..

[2]  Shengyuan Xu,et al.  Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance , 2010 .

[3]  Ju H. Park,et al.  Synchronization of discrete-time neural networks with time delays subject to missing data , 2013, Neurocomputing.

[4]  Hongye Su,et al.  Adaptive almost surely asymptotically synchronization for stochastic delayed neural networks with Markovian switching , 2013 .

[5]  Wuneng Zhou,et al.  Mixed time-delays dependent exponential stability for uncertain stochastic high-order neural networks , 2009, Appl. Math. Comput..

[6]  Yuhua Xu,et al.  Adaptive synchronization for stochastic T-S fuzzy neural networks with time-delay and Markovian jumping parameters , 2013, Neurocomputing.

[7]  Xuerong Mao,et al.  Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching , 2008 .

[8]  Gonzalo Joya,et al.  Hopfield neural networks for optimization: study of the different dynamics , 2002 .

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

[10]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[11]  Zidong Wang,et al.  An LMI approach to stability analysis of stochastic high-order Markovian jumping neural networks with mixed time delays , 2008 .

[12]  Jinde Cao,et al.  Synchronization control of stochastic delayed neural networks , 2007 .

[13]  Jinde Cao,et al.  Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Sabri Arik,et al.  Global stability analysis of neural networks with multiple time varying delays , 2005, IEEE Transactions on Automatic Control.

[15]  Qiankun Song,et al.  Synchronization analysis of coupled connected neural networks with mixed time delays , 2009, Neurocomputing.

[16]  Chuan Ji,et al.  Adaptive exponential synchronization in pth moment of neutral-type neural networks with time delays and Markovian switching , 2013 .

[17]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[18]  Yang Tang,et al.  Stability analysis of switched stochastic neural networks with time-varying delays , 2014, Neural Networks.

[19]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[20]  Peng Shi,et al.  Local Synchronization of Chaotic Neural Networks With Sampled-Data and Saturating Actuators , 2014, IEEE Transactions on Cybernetics.

[21]  Jinde Cao,et al.  Synchronization of Randomly Coupled Neural Networks With Markovian Jumping and Time-Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Qingyu Zhu,et al.  Adaptive synchronization for stochastic neural networks of neutral-type with mixed time-delays , 2013, Neurocomputing.

[23]  Chi-Chuan Hwang,et al.  Globally Asymptotic Stability of a Class of Neutral-Type Neural Networks With Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Zidong Wang,et al.  Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays , 2013, IEEE Transactions on Cybernetics.

[25]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[26]  Rathinasamy Sakthivel,et al.  Robust exponential stability and H ∞ control for switched neutral‐type neural networks , 2014 .

[27]  Yan Gao,et al.  Mode and Delay-Dependent Adaptive Exponential Synchronization in $p$th Moment for Stochastic Delayed Neural Networks With Markovian Switching , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[28]  Chunmei Duan,et al.  Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity , 2009, Neurocomputing.

[29]  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).

[30]  Peng Shi,et al.  Exponential Synchronization of Neural Networks With Discrete and Distributed Delays Under Time-Varying Sampling , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Haijun Jiang,et al.  Finite-time synchronization of delayed neural networks with Cohen-Grossberg type based on delayed feedback control , 2014, Neurocomputing.

[32]  Shengyuan Xu,et al.  Asymptotic Tracking Control of Uncertain Nonlinear Systems With Unknown Actuator Nonlinearity , 2014, IEEE Transactions on Automatic Control.

[33]  Peng Shi,et al.  Exponential $\mathcal {H}_{\infty }$ Filtering for Discrete-Time Switched Neural Networks With Random Delays , 2015, IEEE Transactions on Cybernetics.

[34]  Hong Qiao,et al.  A reference model approach to stability analysis of neural networks , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[35]  Qiankun Song,et al.  Design of controller on synchronization of chaotic neural networks with mixed time-varying delays , 2009, Neurocomputing.

[36]  Yang Tang,et al.  Stability of delayed neural networks with time-varying impulses , 2012, Neural Networks.

[37]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

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