Minimal eventually positive realizations of externally positive systems
2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 68, 140-147 p.Article in journal (Refereed) Published
It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.
Place, publisher, year, edition, pages
Pergamon Press, 2016. Vol. 68, 140-147 p.
Positive linear systems;Minimal realization;Eventually positive matrices;Perron–Frobenius theorem
IdentifiersURN: urn:nbn:se:liu:diva-127609DOI: 10.1016/j.automatica.2016.01.072ISI: 000375507600016OAI: oai:DiVA.org:liu-127609DiVA: diva2:925899
Funding agencies: Swedish Research Council [2015-04390]2016-05-032016-05-032016-06-10