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.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Willem Esterhuizen http://orcid.org/0000-0002-5837-5601
Qing-Guo Wang http://orcid.org/0000-0002-3672-3716