Stabilization of discrete-time switched singular systems with state, output and switching delays. Issue 4 (March 2019)

• Record Type: Journal Article
• Authors: Lin, Jinxing; Zhao, Xudong; Xiao, Min; Shen, Jingjin
• Is Part Of: Journal of the Franklin Institute. Volume 356:Issue 4(2019)
• Page Start: 2060
• Page End: 2089
• Publication Date: 2019-03
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2018.11.034
• Languages: English
• ISSNs: 0016-0032

Abstract

Highlights: We address the problem of feedback stabilization of discrete-time switched singular systems with multiple kinds of delays. Not only the state delay and the measurement output delay of the plant but also the delay in the switching signal of the switched controller is considered. An approach of jointly designing a class of average dwell time switching signals and a switched state feedback stabilizing controller is given. Abstract: This paper is concerned with state feedback stabilization of discrete-time switched singular systems with time-varying delays existing simultaneously in the state, the output and the switching signal of the switched controller. On the basis of equivalent dynamics decomposition and Lyapunov–Krasovskii method, exponential estimates for the response of slow states of the closed-loop subsystems running in asynchronous and synchronous periods are first given. Exponential estimates for the response of fast states are also provided by establishing an analytic equation to solve the fast states and using some algebraic techniques. Then, by employing the obtained exponential estimates and the piecewise Lyapunov function approach with average dwell time (ADT) switching, sufficient conditions for the existence of a class of stabilizing switching signals and state feedback gains are derived, which explicitly depend on upper bounds on the delays and a lower bound on the ADT. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.