Brief paper: The minimal disturbance invariant set: Outer approximations via its partial sums

Authors:
Chong-Jin Ong;Elmer G. Gilbert
Affiliations:
Department of Mechanical Engineering, National University of Singapore and Singapore-MIT Alliance, Singapore;Department of Aerospace Engineering, University of Michigan, Ann Arbor, USA
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

This paper is concerned with outer approximations of the minimal disturbance invariant set (MDIS) of a discrete-time linear system with an additive set-bounded disturbance. The k-step disturbance reachable sets (Minkowski partial sums) are inner approximations of MDIS that converge to MDIS. Enlarged by a suitable scaling, they can lead to outer approximations of MDIS. Three families of approximations, each based on partial sums, are considered. Theoretical properties of the families are proved and interrelated. Algorithmic questions, including error bounds, are addressed. The results are illustrated by computational data from several examples.