Title: Finite-time stability of discrete-time switched singular systems with all unstable modes

Authors: Yijing Wang; Yanchao Zou; Zhiqiang Zuo

Addresses: School of Electrical and Information Engineering, Tianjin Key Laboratory of Process Measurement and Control, Tianjin University, Tianjin 300072, China ' School of Electrical and Information Engineering, Tianjin Key Laboratory of Process Measurement and Control, Tianjin University, Tianjin 300072, China ' School of Electrical and Information Engineering, Tianjin Key Laboratory of Process Measurement and Control, Tianjin University, Tianjin 300072, China

Abstract: The finite-time stability (FTS) problem of discrete-time switched singular systems consisting of all unstable modes is investigated in this paper. By means of dynamic decomposition technique, the original singular system is converted to a reduced-order normal discrete-time switched system. Following the idea of getting into each unstable mode, its internal behaviour is analysed in detail. Two approaches, namely, the Lyapunov one and the state transition matrix one, are utilised to design the switching law with mode-dependent average dwell time such that the FTS property is guaranteed. It is shown that each of them has its own advantages. Selecting appropriate one depends on the specific object for study. In addition, the corresponding asymptotic stability criteria can be easily derived as a by-product. Finally, two examples are given to verify the obtained results and illustrate the effectiveness of the proposed strategies.

Keywords: discrete-time switched singular systems; FTS; finite-time stability; asymptotic stability; MDADT; mode-dependent average dwell time; unstable modes; state transition matrix approach.

DOI: 10.1504/IJSCIP.2017.089814

International Journal of System Control and Information Processing, 2017 Vol.2 No.2, pp.142 - 164

Received: 16 Jan 2017
Accepted: 30 Jul 2017
Published online: 12 Feb 2018 *

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