Minimal eventually positive realizations of externally positive systems
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Claudio Altafini [1]
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[1] Linköping University,Sweden
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- Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 68, 2016, págs. 140-147
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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.
