2005/03/31 by Ricardo David Katz · 2 citations
Computer Science · Engineering · Mathematics · #Formal Methods in Verification #Petri Nets in System Modeling #Stability and Control of Uncertain Systems #math.OC #msc:06F05 #msc:93B27
paper · pdf · doi:10.1109/tac.2006.890478
published as IEEE Transactions on Automatic Control, volume 52 (2007), number 2, pages 229--241 · 24 pages, 1 Postscript figure, proof of Lemma 1 and some references added
openalex publication_date 2007/02/01 · arxiv created 2007/04/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical systems over rings, it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings. Sufficient conditions are given for computing the maximal (A,B)-invariant subspace contained in a given space and the existence of linear state feedbacks is discussed. An application to the study of transportation networks which evolve according to a timetable is considered.