(A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems

C. E. T. Dórea and J. C. Hennet
Additional contact information
C. E. T. Dórea: Universidade Federal de Bahia, Salvador
J. C. Hennet: Centre National de la Recherche Scientifique

Journal of Optimization Theory and Applications, 1999, vol. 103, issue 3, No 2, 542 pages

Abstract: Abstract The problem of confining the trajectory of a linear discrete-time system in a given polyhedral domain is addressed through the concept of (A, B)-invariance. First, an explicit characterization of (A, B)-invariance of convex polyhedra is proposed. Such characterization amounts to necessary and sufficient conditions in the form of linear matrix relations and presents two major advantages compared to the ones found in the literature: it applies to any convex polyhedron and does not require the computation of vertices. Such advantages are felt particularly in the computation of the supremal (A, B)-invariant set included in a given polyhedron, for which a numerical method is proposed. The problem of computing a control law which forces the system trajectories to evolve inside an (A, B)-invariant polyhedron is treated as well. Finally, the (A, B)-invariance relations are generalized to persistently disturbed systems.

Keywords: Linear systems; linear programming; convexity; polyhedra; invariance (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1021727806358 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:103:y:1999:i:3:d:10.1023_a:1021727806358

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/A:1021727806358

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().