Finite-time stability and stabilisation with polyhedral domains for linear systems. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Esterhuizen, Willem; Wang, Qing-Guo
• Is Part Of: International journal of control. Volume 93:Issue 9(2020)
• Page Start: 2086
• Page End: 2094
• Publication Date: 2020-09-01
• Subjects: Finite-time stability -- polyhedral constraints -- analysis of systems with uncertainties -- feedback stabilization; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1541364
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: This paper deals with finite-time stability, boundedness and stabilisation of discrete-time linear systems with regards to polyhedral domains. The key observation made in this paper is that finite-time stability properties can be analysed in terms of reachable sets. We first establish necessary and sufficient conditions for finite-time stability and boundedness of nominal systems, expressible as linear programming problems. We then present sufficient conditions that may be used to compute feedback control to render such systems finite-time stable/bounded. Finally we generalise the above results to the case of discrete-time linear systems with polytopic uncertainty subject to a bounded disturbance.