Projective lag synchronization of Markovian jumping neural networks with mode-dependent mixed time-delays based on an integral sliding mode controller

In this paper, the mode-dependent projective synchronization problem of stochastic neural networks with mixed time-delays is investigated. By considering a proper sliding model surface, a sliding mode controller (SMC) is synthesized to guarantee the reach-ability of the specified sliding surface. The globally asymptotically stable of the sliding mode dynamical system is surveyed with the Lyapunov stability theory and linear matrix inequality (LMI) technique. A sufficient projective synchronization criterion for the stochastic neural networks is derived. Finally, numerical simulations are exploited to illustrate the effectiveness of the main results.

[1]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[2]  Hamid Reza Karimi,et al.  Control design for a hypersonic aircraft using a switched linear parameter-varying system approach , 2013, J. Syst. Control. Eng..

[3]  Cuihong Wang,et al.  Terminal Sliding Mode Control for Singular Systems with Unmatched Uncertainties , 2007, 2007 IEEE International Conference on Control and Automation.

[4]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[5]  Hongyi Li,et al.  Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters , 2008 .

[6]  Pengcheng Wei,et al.  Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control , 2011 .

[7]  Santo Banerjee,et al.  Generalized and projective synchronization in modulated time-delayed systems , 2010 .

[8]  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.

[9]  J. M. González-Miranda,et al.  Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving , 1998 .

[10]  Ligang Wu,et al.  Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems , 2008, J. Frankl. Inst..

[11]  A. I. Matasov,et al.  Neutral Stochastic Differential Delay Equations with Markovian Switching , 2003 .

[12]  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).

[13]  Qian Ma,et al.  Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities , 2011, Neurocomputing.

[14]  Jian Xu,et al.  Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller , 2010, Appl. Math. Comput..

[15]  Chuandong Li,et al.  Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication , 2004 .

[16]  Jinde Cao,et al.  Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch , 2011, Nonlinear Dynamics.

[17]  Ned J Corron,et al.  Lag and anticipating synchronization without time-delay coupling. , 2005, Chaos.

[18]  Xiaodi Li,et al.  Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays , 2012, J. Optim. Theory Appl..

[19]  Zhidong Teng,et al.  Adaptive synchronization of neural networks with time-varying delay and distributed delay , 2008 .

[20]  Jinde Cao,et al.  Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays , 2011 .

[21]  Yonghui Sun,et al.  Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation , 2007 .

[22]  Jinde Cao,et al.  Synchronization analysis of singular hybrid coupled networks , 2008 .

[23]  Yi Chai,et al.  Modified Function Projective Synchronization of Chaotic Neural Networks with Delays Based on Observer , 2011 .

[24]  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.

[25]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[26]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[27]  Ke Qin,et al.  Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller , 2014, Neurocomputing.

[28]  Zidong Wang,et al.  Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays , 2012, Neurocomputing.

[29]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[30]  D. H. Ji,et al.  Synchronization of singular complex dynamical networks with time-varying delays , 2010, Appl. Math. Comput..

[31]  Guoliang Cai,et al.  Adaptive Projective Synchronization in An Array of Asymmetric Neural Networks , 2012, J. Comput..

[32]  Jinde Cao,et al.  Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters , 2008 .

[33]  Haijun Jiang,et al.  Projective synchronization for fractional neural networks , 2014, Neural Networks.

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

[35]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[36]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Yan Liu,et al.  Stochastic asymptotic stability of Markovian jumping neural networks with Markov mode estimation and mode-dependent delays , 2009 .

[38]  X. Mao,et al.  Stochastic differential delay equations with Markovian switching , 2000 .

[39]  Qing-Long Han,et al.  On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty , 2004, Autom..

[40]  Wanyu Liu,et al.  Robust function projective synchronization of a class of uncertain chaotic systems , 2009 .

[41]  Hongjie Li,et al.  Cluster synchronization stability for stochastic complex dynamical networks with probabilistic interval time-varying delays , 2011 .

[42]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[43]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[44]  Zhaolin Cheng,et al.  Delay-Dependent Robust Stability Criteria for Two Classes of Uncertain Singular Time-Delay Systems , 2007, IEEE Transactions on Automatic Control.

[45]  Li Sheng,et al.  Robust stability of Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent delays , 2013, Int. J. Syst. Sci..

[46]  Qingyu Zhu,et al.  Mode-dependent projective synchronization for neutral-type neural networks with distributed time-delays , 2014, Neurocomputing.

[47]  Yong Chen,et al.  Generalized Q-S (lag, anticipated and complete) synchronization in modified Chua's circuit and Hindmarsh-Rose systems , 2006, Appl. Math. Comput..

[48]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[49]  X. Lou,et al.  Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters , 2009 .

[50]  Nastaran Vasegh,et al.  Projective synchronization of chaotic time-delayed systems via sliding mode controller , 2009 .

[51]  Mao-Yin Chen,et al.  Synchronization in Complex Dynamical Networks With Random Sensor Delay , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[52]  James Lam,et al.  Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions , 2010, IEEE Transactions on Automatic Control.