title: Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations.
abstract: In this paper, the problem of finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations is investigated. By constructing a novel Lyapunov-Krasovskii functional and employing a new summation inequality named discrete Wirtinger-based inequality, reciprocally convex approach and zero equality, the improved finite-time stability criteria are derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold when fixed time interval. Furthermore, the obtained conditions are formulated in forms of linear matrix inequalities which can be solved by using some standard numerical packages. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.
authors.affiliation: School of Information Engineering, Fuyang Normal College, Fuyang 236041, PR China; School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China. Electronic address: kangwei0830@163.com.
authors.forename: Wei
authors.initials: W
authors.lastname: Kang
authors.affiliation: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China.
authors.forename: Shouming
authors.initials: S
authors.lastname: Zhong
authors.affiliation: School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, PR China.
authors.forename: Kaibo
authors.initials: K
authors.lastname: Shi
authors.affiliation: School of Science, Hubei University for Nationalities, Enshi 44500, PR China.
authors.forename: Jun
authors.initials: J
authors.lastname: Cheng
keywords: Discrete-time system; Finite-time stability; Nonlinear perturbations; Time-varying delay