Journal Article

Exploring positively invariant sets by linear systems over idempotent semirings

L. Truffet

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 3, pages 307-322
Published in print September 2004 | ISSN: 0265-0754
Published online September 2004 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/21.3.307
Exploring positively invariant sets by linear systems over idempotent semirings

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It is now almost well‐known that linear systems over idempotent semirings modelize Discrete Event Systems of practical interest. The control of such systems is a recent topic of research which has not yet been as developed control theory in classical algebra. The properties of positively invariant sets are involved in many different problems in classical control theory, such as constrained control, robustness analysis and optimization, and also in aggregation of Markov chains (namely strong lumpability and coherency).

In this paper we identify special families of positively invariant sets for linear discrete‐time systems over idempotent semirings. Necessary and sufficient conditions for a given set to be a positively invariant set of a linear system are obtained. The results obtained lead to further works on this subject.

Keywords: max‐plus algebra; system control theory; Lyapunov method

Journal Article.  0 words. 

Subjects: Mathematics

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