Journal Article

Invariant polytopes of linear systems

LORENZO FARINA and LUCA BENVENUTI

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 15, issue 3, pages 233-240
Published in print September 1998 | ISSN: 0265-0754
Published online September 1998 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/15.3.233
Invariant polytopes of linear systems

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Stable linear systems possess invariant sets which have hyperellipsoidal regions associated with their Lyapunov function. In real systems, however, state and control variables are often confined in bounded polyhedral regions(polytopes) so that a set of linear inequalities has to be satisfied. In this paper, necessary and sufficient conditions for the existence of positively invariant polytopes for both discrete-time and continuous-time linear systems are given in terms of their spectral properties.

Journal Article.  0 words. 

Subjects: Mathematics

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