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

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. Key words: Disturbance invariant sets, linear control systems, Minkowski sum.

• Type: Journal
• Year: 2006
• Where: AUTOMATICA
• Authors: Chong Jin Ong, Elmer G. Gilbert
• Keywords: AUTOMATICA 2006, Invariant Sets, Outer Approximations, Partial Sums