Finite-time stability and stabilisation with polyhedral domains for linear systems

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.

KEYWORDS:

• Finite-time stability
• polyhedral constraints
• analysis of systems with uncertainties
• feedback stabilization

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

Additional information

Funding

Qing-Guo WANG acknowledges the financial support of the National Research Foundation of South Africa (Grant Number: 113340), which partially funded his research on this work.