title: Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information.
abstract: In this paper, synchronization in an array of discrete-time neural networks (DTNNs) with time-varying delays coupled by Markov jump topologies is considered. It is assumed that the switching information can be collected by a tracker with a certain probability and transmitted from the tracker to controller precisely. Then the controller selects suitable control gains based on the received switching information to synchronize the network. This new control scheme makes full use of received information and overcomes the shortcomings of mode-dependent and mode-independent control schemes. Moreover, the proposed control method includes both the mode-dependent and mode-independent control techniques as special cases. By using linear matrix inequality (LMI) method and designing new Lyapunov functionals, delay-dependent conditions are derived to guarantee that the DTNNs with Markov jump topologies to be asymptotically synchronized. Compared with existing results on Markov systems which are obtained by separately using mode-dependent and mode-independent methods, our result has great flexibility in practical applications. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.
authors.affiliation: Department of Mathematics, Chongqing Normal University, Chongqing 401331, China. Electronic address: xinsongyang@163.com.
authors.forename: Xinsong
authors.initials: X
authors.lastname: Yang
authors.affiliation: Department of Mathematics, Chongqing Normal University, Chongqing 401331, China. Electronic address: scholarcqnu12@163.com.
authors.forename: Zhiguo
authors.initials: Z
authors.lastname: Feng
authors.affiliation: College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China. Electronic address: fengjw@szu.edu.cn.
authors.forename: Jianwen
authors.initials: J
authors.lastname: Feng
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China. Electronic address: jdcao@seu.edu.cn.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
mesh_terms: D000465:Algorithms; D006801:Humans; D008390:Markov Chains; D016571:Neural Networks, Computer; D011336:Probability; D013997:Time Factors
keywords: Discrete-time neural networks; Markov jump coupling; Synchronization; Time-varying delay