Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations

Wei Kang; Shouming Zhong; Kaibo Shi; Jun Cheng

doi:10.1016/j.isatra.2015.11.006

Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations

ISA Trans. 2016 Jan:60:67-73. doi: 10.1016/j.isatra.2015.11.006. Epub 2015 Nov 29.

Authors

Wei Kang¹, Shouming Zhong², Kaibo Shi³, Jun Cheng⁴

Affiliations

¹ 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.
² School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China.
³ School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, PR China.
⁴ School of Science, Hubei University for Nationalities, Enshi 44500, PR China.

PMID: 26619938
DOI: 10.1016/j.isatra.2015.11.006

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.

Keywords: Discrete-time system; Finite-time stability; Nonlinear perturbations; Time-varying delay.

Publication types

Research Support, Non-U.S. Gov't