Positively invariant sets for continuous-time systems with the cone-preserving property
作者:
S. TARBOURIECH,
C. BURGAT,
期刊:
International Journal of Systems Science
(Taylor Available online 1993)
卷期:
Volume 24,
issue 6
页码: 1037-1047
ISSN:0020-7721
年代: 1993
DOI:10.1080/00207729308949542
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The main objective of this paper is to determine positively invariant and asymptotically stable polyhedral sets for a linear continuous-time system ẋ(t) =Ax(t) for which matrixe1Ais a cone-preserving matrix, that is,e1AK⊂K, for some proper coneK. Necessary and sufficient conditions guaranteeing that some bounded sets are positively invariant and contractive are given. These sets are obtained by means of the intersection of shifted cones. First, some results presented under a geometrical form and also in algebraic form allow characterization of systems having the cone-preserving property. Finally, as an application, the proposed results are used to determine a stability domain for a state feedback regulator with constraints on either or both states and controls.
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