title: Mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching based on vector Lyapunov functions.
abstract: This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results.
authors.affiliation: College of Science, Hohai University, Nanjing, 210098, China. Electronic address: 1575388989@qq.com.
authors.forename: Zhihong
authors.initials: Z
authors.lastname: Li
authors.affiliation: College of Science, Hohai University, Nanjing, 210098, China. Electronic address: liulei_hust@hhu.edu.cn.
authors.forename: Lei
authors.initials: L
authors.lastname: Liu
authors.affiliation: School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, China; Department of Mathematics, University of Bielefeld, Bielefeld D-33615, Germany. Electronic address: zqx22@126.com.
authors.forename: Quanxin
authors.initials: Q
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008390:Markov Chains; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: -matrix; Cohen–Grossberg neural network; Exponential input-to-state stability; Halanay inequality; Markovian switching; Time delay