Exponential synchronization of chaotic neural networks with time-varying delay via intermittent output feedback approach

This paper is dealt with the problem of exponential synchronization for chaotic neural networks with time-varying delay by using intermittent output feedback control. Based on the Lyapunov–Krasovskii functional method and the lower bound lemma for reciprocally convex technique, a novel criterion for existence of the controller is first established to ensure synchronization between the master and slave systems. Moreover, from the delay point of view, the derived criterion is extended to the relaxed case because of introducing an adjustable parameter in the Lyapunov–Krasovskii functional. Finally, a numerical simulation is carried out to demonstrate the effectiveness of the proposed synchronization law.

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

[2]  Huibin Zhu,et al.  Stabilization and synchronization of chaotic systems via intermittent control , 2010 .

[3]  Ju H. Park,et al.  Dynamic output-feedback-based H∞ design for networked control systems with multipath packet dropouts , 2016, Appl. Math. Comput..

[4]  Dan Ye,et al.  A Separated Approach to Control of Markov Jump Nonlinear Systems With General Transition Probabilities , 2016, IEEE Transactions on Cybernetics.

[5]  Yi Zhao,et al.  Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control , 2016, Appl. Math. Comput..

[6]  Min Wu,et al.  Asymptotical synchronization for chaotic Lur'e systems using sampled-data control , 2013, Commun. Nonlinear Sci. Numer. Simul..

[7]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[8]  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.

[9]  Qing-Long Han,et al.  Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays , 2011, IEEE Trans. Neural Networks.

[10]  Qiankun Song,et al.  Stabilization and synchronization of chaotic systems with mixed time-varying delays via intermittent control with non-fixed both control period and control width , 2015, Neurocomputing.

[11]  Chuandong Li,et al.  Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period , 2016, Neurocomputing.

[12]  Taishin Nomura,et al.  Modeling human postural sway using an intermittent control and hemodynamic perturbations. , 2013, Mathematical biosciences.

[13]  Chuandong Li,et al.  Stabilization of Nonlinear Systems via Periodically Intermittent Control , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[15]  Zhidong Teng,et al.  Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control , 2010 .

[16]  T. Liao,et al.  H∞ synchronization of chaotic systems using output feedback control design , 2007 .

[17]  Bo Zhang,et al.  Adaptive synchronization of Cohen-Grossberg neural network with mixed time-varying delays and stochastic perturbation , 2015, Appl. Math. Comput..

[18]  Chuandong Li,et al.  Exponential stabilization of chaotic systems with delay by periodically intermittent control. , 2007, Chaos.

[19]  Qing-Guo Wang,et al.  Mode-dependent filter design for Markov jump systems with sensor nonlinearities in finite frequency domain , 2017, Signal Process..

[20]  Ju H. Park,et al.  A novel Lyapunov functional for stability of time-varying delay systems via matrix-refined-function , 2017, Autom..

[21]  Xin-Ping Guan,et al.  Stability analysis of time-delay systems via free-matrix-based double integral inequality , 2017, Int. J. Syst. Sci..

[22]  Xin-Ping Guan,et al.  Synchronization of Chaotic Lur’e Systems With Time Delays Using Sampled-Data Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Hao Shen,et al.  Finite-Time Cluster Synchronization of Lur’e Networks: A Nonsmooth Approach , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  V. Kapila,et al.  Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators , 2010 .

[25]  Ju H. Park,et al.  Extended Dissipative Analysis for Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

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

[27]  Shen Yan,et al.  Finite-time H∞ static output control of Markov jump systems with an auxiliary approach , 2016, Appl. Math. Comput..

[28]  Jinde Cao,et al.  Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays , 2015, Appl. Math. Comput..

[29]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..

[30]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[31]  Guodong Zhang,et al.  Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Yong He,et al.  Exponential stabilization of neural networks with time-varying delay by periodically intermittent control , 2016, Neurocomputing.

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

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

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

[36]  Xin-Ping Guan,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Peter J. Gawthrop,et al.  Open-loop intermittent feedback control: practical continuous-time GPC , 1999 .

[38]  Ju H. Park,et al.  New delay-partitioning approaches to stability criteria for uncertain neutral systems with time-varying delays , 2012, J. Frankl. Inst..

[39]  Min Wu,et al.  Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach , 2017, Appl. Math. Comput..

[40]  Kanjian Zhang,et al.  Synchronization control of recurrent neural networks with distributed delays , 2008 .

[41]  Xian Zhang,et al.  Exponential Stabilization of Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays by Intermittent Control: A CCL Approach , 2014, Circuits Syst. Signal Process..

[42]  Ju H. Park,et al.  Impulsive Effects on Quasi-Synchronization of Neural Networks With Parameter Mismatches and Time-Varying Delay , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[44]  Wang Yi-jing,et al.  Exponential Synchronization of Master-Slave Lur'e Systems via Intermittent Time-Delay Feedback Control , 2010 .

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

[46]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[47]  Peng Shi,et al.  Exponential Stabilization for Sampled-Data Neural-Network-Based Control Systems , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[48]  Cheng-Chew Lim,et al.  Reliable H ∞ static output control of linear time‐varying delay systems against sensor failures , 2017 .

[49]  Yasuyuki Inoue,et al.  Adaptive intermittent control: A computational model explaining motor intermittency observed in human behavior , 2015, Neural Networks.

[50]  Yong He,et al.  Stability analysis of systems with time-varying delay via relaxed integral inequalities , 2016, Syst. Control. Lett..

[51]  J. Kurths,et al.  Single impulsive controller for globally exponential synchronization of dynamical networks , 2013 .

[52]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[53]  Xinzhi Liu,et al.  Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control , 2012 .

[54]  Shengyuan Xu,et al.  Relaxed conditions for stability of time-varying delay systems , 2017, Autom..

[55]  Ju H. Park,et al.  Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control , 2014 .

[56]  Chen Xu,et al.  Exponential synchronization of stochastic perturbed complex networks with time-varying delays via periodically intermittent pinning , 2013, Commun. Nonlinear Sci. Numer. Simul..

[57]  Kok Lay Teo,et al.  Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays☆ , 2005 .

[58]  Jinde Cao,et al.  Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control , 2014, Neurocomputing.