Nonfragile Exponential Synchronization of Delayed Complex Dynamical Networks With Memory Sampled-Data Control

This paper considers nonfragile exponential synchronization for complex dynamical networks (CDNs) with time-varying coupling delay. The sampled-data feedback control, which is assumed to allow norm-bounded uncertainty and involves a constant signal transmission delay, is constructed for the first time in this paper. By constructing a suitable augmented Lyapunov function, and with the help of introduced integral inequalities and employing the convex combination technique, a sufficient condition is developed, such that the nonfragile exponential stability of the error system is guaranteed. As a result, for the case of sampled-data control free of norm-bound uncertainties, some sufficient conditions of sampled-data synchronization criteria for the CDNs with time-varying coupling delay are presented. As the formulations are in the framework of linear matrix inequality, these conditions can be easily solved and implemented. Two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control.

[1]  Jinde Cao,et al.  Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Ju H. Park,et al.  H∞ tracking of uncertain stochastic time-delay systems: Memory state-feedback controller design , 2014, Appl. Math. Comput..

[3]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[4]  Peng Shi,et al.  Adaptive Sliding-Mode Control of Markov Jump Nonlinear Systems With Actuator Faults , 2017, IEEE Transactions on Automatic Control.

[5]  Bo Song,et al.  Exponential synchronization for complex dynamical networks with sampled-data , 2012, J. Frankl. Inst..

[6]  Shengyuan Xu,et al.  Robust Exponential Stability of Uncertain Stochastic Neural Networks With Distributed Delays and Reaction-Diffusions , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Yonggui Kao,et al.  A sliding mode approach to H∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems , 2015, Autom..

[8]  Guang-Hong Yang,et al.  Adaptive Fault-Tolerant Synchronization Control of a Class of Complex Dynamical Networks With General Input Distribution Matrices and Actuator Faults , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Rathinasamy Sakthivel,et al.  Robust sampled-data H∞ control for mechanical systems , 2015, Complex..

[10]  Ligang Wu,et al.  Fuzzy Tracking Control for Nonlinear Networked Systems , 2017, IEEE Transactions on Cybernetics.

[11]  Ligang Wu,et al.  Event-Triggered Control for Nonlinear Systems Under Unreliable Communication Links , 2017, IEEE Transactions on Fuzzy Systems.

[12]  S. M. Lee,et al.  Improved results on sampled-data synchronization of complex dynamical networks with time-varying coupling delay , 2015 .

[13]  Guang-Hong Yang,et al.  Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Dan Zhang,et al.  Nonfragile Distributed Filtering for T–S Fuzzy Systems in Sensor Networks , 2015, IEEE Transactions on Fuzzy Systems.

[15]  Lijie Wang,et al.  Adaptive Fuzzy Control of Nonlinear Systems With Unmodeled Dynamics and Input Saturation Using Small-Gain Approach , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[16]  Peng Shi,et al.  Sampled-Data Exponential Synchronization of Complex Dynamical Networks With Time-Varying Coupling Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[18]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[19]  Rathinasamy Sakthivel,et al.  Non-fragile synchronization of memristive BAM networks with random feedback gain fluctuations , 2015, Commun. Nonlinear Sci. Numer. Simul..

[20]  Huijun Gao,et al.  Pinning Distributed Synchronization of Stochastic Dynamical Networks: A Mixed Optimization Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[21]  E. Fridman,et al.  Networked‐based stabilization via discontinuous Lyapunov functionals , 2012 .

[22]  Renquan Lu,et al.  Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling , 2015, Syst. Control. Lett..

[23]  Jinde Cao,et al.  Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[25]  Huaguang Zhang,et al.  Sampled-data synchronization for complex networks based on discontinuous LKF and mixed convex combination , 2015, J. Frankl. Inst..

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

[27]  Wai Keung Wong,et al.  Distributed Synchronization of Coupled Neural Networks via Randomly Occurring Control , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[28]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[29]  Hao Shen,et al.  Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control , 2015, Appl. Math. Comput..

[30]  Nan Li,et al.  Synchronization for general complex dynamical networks with sampled-data , 2011, Neurocomputing.

[31]  Lijie Wang,et al.  Adaptive Fuzzy Control for Nonstrict-Feedback Systems With Input Saturation and Output Constraint , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[32]  Guang-Hong Yang,et al.  Nonfragile $H_{\infty}$ Filter Design for T–S Fuzzy Systems in Standard Form , 2014, IEEE Transactions on Industrial Electronics.

[33]  Huai-Ning Wu,et al.  Pinning Control Strategies for Synchronization of Linearly Coupled Neural Networks With Reaction–Diffusion Terms , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[35]  Yuechao Ma,et al.  H ∞ robust exponential stability and memory state feedback control for uncertain singular time-delay systems with saturating actuators , 2016 .

[36]  Wei Xing Zheng,et al.  Synchronization and State Estimation of a Class of Hierarchical Hybrid Neural Networks With Time-Varying Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Yong-Ki Ma,et al.  Reliable anti-synchronization conditions for BAM memristive neural networks with different memductance functions , 2016, Appl. Math. Comput..

[38]  Yuxin Zhao,et al.  Resilient Asynchronous $H_{\infty }$ Filtering for Markov Jump Neural Networks With Unideal Measurements and Multiplicative Noises , 2015, IEEE Transactions on Cybernetics.

[39]  Xinmin Song,et al.  Linear quadratic Gaussian control for linear time-delay systems , 2014 .

[40]  Guo-Ping Jiang,et al.  A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..