Exponential synchronization of discrete-time impulsive dynamical networks with time-varying delays and stochastic disturbances

Abstract In this paper, based on the discrete-time delayed impulsive system theory, exponential synchronization of discrete-time complex networks with both time-varying delays and stochastic disturbances is investigated. By applying an iterative Lyapunov function in combination with the linear matrix inequality (LMI) technique, a new synchronization criterion based on topology matrices and impulsive conditions is developed. Some numerical simulations are provided to verify the theoretical results.

[1]  Gai Sun,et al.  Exponential stability of impulsive discrete-time stochastic BAM neural networks with time-varying delay , 2014, Neurocomputing.

[2]  Zengrong Liu,et al.  Robust impulsive synchronization of complex delayed dynamical networks , 2008 .

[3]  Jin Zhou,et al.  Synchronization in complex delayed dynamical networks with impulsive effects , 2007 .

[4]  Zidong Wang,et al.  Robust stability of discrete-time stochastic neural networks with time-varying delays , 2008, Neurocomputing.

[5]  Zidong Wang,et al.  Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling , 2012, IEEE Transactions on Automatic Control.

[6]  Xinchu Fu,et al.  On pinning control of some typical discrete-time dynamical networks , 2010 .

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[9]  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.

[10]  Jinde Cao,et al.  Robust impulsive synchronization of coupled delayed neural networks with uncertainties , 2007 .

[11]  Chuandong Li,et al.  Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: A Razumikhin approach , 2012, Neurocomputing.

[12]  Habib Fardoun,et al.  Exponential synchronization for a class of impulsive networks with time-delays based on single controller , 2016, Neurocomputing.

[13]  Jie Huang,et al.  Two consensus problems for discrete-time multi-agent systems with switching network topology , 2012, Autom..

[14]  Tingwen Huang,et al.  Event-triggered H∞ state estimation for discrete-time neural networks with mixed time delays and sensor saturations , 2017, Neural Computing and Applications.

[15]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[16]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[17]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[18]  Yan‐Wu Wang,et al.  Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays , 2010 .

[19]  Zhen Li,et al.  Exponential synchronization of impulsive discrete-time complex networks with time-varying delay , 2015, Neurocomputing.

[20]  Zengrong Liu,et al.  Impulsive synchronization seeking in general complex delayed dynamical networks , 2011 .

[21]  Xinzhi Liu,et al.  Uniform asymptotic stability of impulsive discrete systems with time delay , 2011 .

[22]  Beom Jun Kim,et al.  Synchronization on small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[24]  Jürgen Kurths,et al.  Synchronization between two coupled complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Lin Wang,et al.  Controllability of networked MIMO systems , 2015, Autom..

[26]  Yu Zhang Exponential stability of impulsive discrete systems with time delays , 2012, Appl. Math. Lett..

[27]  Ralph R. Martin,et al.  Discrete-time BAM neural networks with variable delays , 2007 .

[28]  Tingwen Huang,et al.  Passivity-based synchronization of a class of complex dynamical networks with time-varying delay , 2015, Autom..

[29]  Xia Li,et al.  Asynchronously switched control of discrete impulsive switched systems with time delays , 2013, Inf. Sci..

[30]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[31]  Hong Qiao,et al.  Event-Triggered State Estimation for Discrete-Time Multidelayed Neural Networks With Stochastic Parameters and Incomplete Measurements , 2017, IEEE Transactions on Neural Networks and Learning Systems.

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

[33]  Wai Keung Wong,et al.  Impulsive pinning synchronization of stochastic discrete-time networks , 2010, Neurocomputing.

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