Non-fragile mixed H∞ and passive synchronization of Markov jump neural networks with mixed time-varying delays and randomly occurring controller gain fluctuation

This paper studies the non-fragile mixed H∞ and passive synchronization problem for Markov jump neural networks. The randomly occurring controller gain fluctuation phenomenon is investigated for non-fragile strategy. Moreover, the mixed time-varying delays composed of discrete and distributed delays are considered. By employing stochastic stability theory, synchronization criteria are developed for the Markov jump neural networks. On the basis of the derived criteria, the non-fragile synchronization controller is designed. Finally, an illustrative example is presented to demonstrate the validity of the control approach.

[1]  Yong Xu,et al.  The Phase Transition in a Bistable Duffing System Driven by Lévy Noise , 2015 .

[2]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[3]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

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

[5]  Huiqing Zhang,et al.  Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise , 2013 .

[6]  Yong Xu,et al.  Lévy noise induced stochastic resonance in an FHN model , 2016 .

[7]  Jinde Cao,et al.  Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification , 2007 .

[8]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[9]  A. Arunkumar,et al.  Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks. , 2014, ISA transactions.

[10]  Jinde Cao,et al.  Synchronization of Markovian Coupled Neural Networks With Nonidentical Node-Delays and Random Coupling Strengths , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[11]  徐瑞,et al.  Robust synchronization of an array of neural networks with hybrid coupling and mixed time delays , 2014 .

[12]  Huiqing Zhang,et al.  Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise , 2012 .

[13]  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).

[14]  Daniel W. C. Ho,et al.  Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach , 2016, IEEE Transactions on Cybernetics.

[15]  Meikang Qiu,et al.  Exponential ${\rm H}_{\infty}$ Synchronization of General Discrete-Time Chaotic Neural Networks With or Without Time Delays , 2010, IEEE Transactions on Neural Networks.

[16]  Jinde Cao,et al.  Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[18]  Xia Huang,et al.  Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms , 2012 .

[19]  Bo Song,et al.  Mixed H∞ and passive filtering for singular systems with time delays , 2013, Signal Process..

[20]  Daniel W. C. Ho,et al.  Finite-Time Cluster Synchronization of T–S Fuzzy Complex Networks With Discontinuous Subsystems and Random Coupling Delays , 2015, IEEE Transactions on Fuzzy Systems.

[21]  Huijun Gao,et al.  Passivity and Passification for Networked Control Systems , 2007, SIAM J. Control. Optim..

[22]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[23]  Pin-Lin Liu,et al.  Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay. , 2013, ISA transactions.

[24]  Xinsong Yang,et al.  Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects , 2016, IEEE Transactions on Automatic Control.

[25]  Lixiang Li,et al.  Synchronization control of memristor-based recurrent neural networks with perturbations , 2014, Neural Networks.

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

[27]  Guozhen Tan,et al.  Adaptive Cluster Synchronization of Directed Complex Networks with Time Delays , 2014, PloS one.

[28]  Lixian Zhang,et al.  Passivity and passification for Markov jump genetic regulatory networks with time-varying delays , 2014, Neurocomputing.

[29]  Ju H. Park,et al.  Non-fragile synchronization of neural networks with time-varying delay and randomly occurring controller gain fluctuation , 2013, Appl. Math. Comput..

[30]  Guanghong Yang,et al.  Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay , 2008 .

[31]  Xudong Zhao,et al.  New robust delay-dependent stability and H∞ analysis for uncertain Markovian jump systems with time-varying delays , 2010, J. Frankl. Inst..

[32]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[33]  Hao Zhang,et al.  Stability and Synchronization for Discrete-Time Complex-Valued Neural Networks with Time-Varying Delays , 2014, PloS one.

[34]  Zidong Wang,et al.  Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon , 2011, IEEE Transactions on Neural Networks.

[35]  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.

[36]  Yong Xu,et al.  The Availability of Logical Operation Induced by Dichotomous Noise for a Nonlinear Bistable System , 2013, 1309.0904.

[37]  Huiqing Zhang,et al.  Lévy noise induced switch in the gene transcriptional regulatory system. , 2012, Chaos.

[38]  Jinde Cao,et al.  Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information , 2017, Neural Networks.