Delayed impulsive synchronization of discrete-time complex networks with distributed delays

In this paper, a novel delayed impulsive control strategy is proposed for synchronization of discrete-time complex networks with distributed delays. Different from the existing results, the involving time delays include distributed delays and impulsive input delays. Employing the Razumikhin theorem and the mathematical induction method, several sufficient criteria are derived in terms of algebraic conditions, which depend on impulsive input delays and impulsive control gains. Meanwhile, the derived criteria also reveal the relationship between the bounds of impulsive intervals and impulsive input delays. Finally, two examples are given to illustrate the effectiveness of the proposed approach.

[1]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[2]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[3]  Dean S. Clark,et al.  Short proof of a discrete gronwall inequality , 1987, Discret. Appl. Math..

[4]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[5]  L. Chua,et al.  Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication , 1997 .

[6]  Fikret Sivrikaya,et al.  Time synchronization in sensor networks: a survey , 2004, IEEE Network.

[7]  Hongyong Zhao,et al.  Global asymptotic stability of Hopfield neural network involving distributed delays , 2004, Neural Networks.

[8]  Changsong Zhou,et al.  Dynamical weights and enhanced synchronization in adaptive complex networks. , 2006, Physical review letters.

[9]  Gang Zhang,et al.  Synchronization of complex dynamical networks via impulsive control. , 2007, Chaos.

[10]  Horacio J. Marquez,et al.  Razumikhin-type stability theorems for discrete delay systems , 2007, Autom..

[11]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Zidong Wang,et al.  Exponential synchronization of stochastic delayed discrete-time complex networks , 2008 .

[13]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[14]  Yu Zhang,et al.  Impulsive Control of Discrete Systems With Time Delay , 2009, IEEE Transactions on Automatic Control.

[15]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2009, Autom..

[16]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Sarangapani Jagannathan,et al.  Output Feedback Control of a Quadrotor UAV Using Neural Networks , 2010, IEEE Transactions on Neural Networks.

[18]  Zhidong Teng,et al.  Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms , 2010, IEEE Transactions on Neural Networks.

[19]  Jun-an Lu,et al.  Impulsive synchronization of general continuous and discrete-time complex dynamical networks , 2010 .

[20]  Wei Xing Zheng,et al.  Exponential stability of nonlinear time-delay systems with delayed impulse effects , 2011, Autom..

[21]  Chuandong Li,et al.  Stabilizing Effects of Impulses in Discrete-Time Delayed Neural Networks , 2011, IEEE Transactions on Neural Networks.

[22]  Wenbing Zhang,et al.  Exponential stability of stochastic differential delay systems with delayed impulse effects , 2011 .

[23]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[24]  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.

[25]  Huijun Gao,et al.  A Constrained Evolutionary Computation Method for Detecting Controlling Regions of Cortical Networks , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[26]  Wei Xing Zheng,et al.  Delayed Impulsive Control of Takagi–Sugeno Fuzzy Delay Systems , 2013, IEEE Transactions on Fuzzy Systems.

[27]  Yang Tang,et al.  Exponential Synchronization of Coupled Switched Neural Networks With Mode-Dependent Impulsive Effects , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[28]  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.

[29]  C. A. Rabbath,et al.  Discrete-Time Control System Design with Applications , 2013 .

[30]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[31]  J. Kurths,et al.  Pinning controllability of complex networks with community structure. , 2013, Chaos.

[32]  Bin Liu,et al.  Stability of discrete-time delayed impulsive linear systems with application to multi-tracking , 2014, Int. J. Control.

[33]  Feiqi Deng,et al.  Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses , 2013, Commun. Nonlinear Sci. Numer. Simul..

[34]  Yang Tang,et al.  Synchronization of Nonlinear Dynamical Networks With Heterogeneous Impulses , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  R. Rakkiyappan,et al.  Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays , 2014 .

[36]  Wenwu Yu,et al.  Impulsive synchronization schemes of stochastic complex networks with switching topology: Average time approach , 2014, Neural Networks.

[37]  Yu Zhang.  Stability of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities , 2014 .

[38]  Huijun Gao,et al.  Distributed Robust Synchronization of Dynamical Networks With Stochastic Coupling , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  Gang Wang,et al.  Asynchronous control of discrete-time impulsive switched systems with mode-dependent average dwell time. , 2014, ISA transactions.

[40]  Yang Tang,et al.  Synchronization of Stochastic Dynamical Networks Under Impulsive Control With Time Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Tianping Chen,et al.  Synchronization of Nonlinear Coupled Networks via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[42]  Claude H. Moog,et al.  Observability criteria for impulsive control systems with applications to biomedical engineering processes , 2015, Autom..

[43]  Jinde Cao,et al.  Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays , 2015, Neural Networks.

[44]  Ju H. Park,et al.  Non-fragile synchronization control for complex networks with additive time-varying delays , 2015, Complex..