State space realization of even generalized positive and odd rational function. Applications to static output feedback

2012/02/06 by Daniel Alpay, Alpay, Daniel, Izchak Lewkowicz +1
Engineering · Mathematics · #15B48 #26C15 #47L07 #93B15 (Primary) 15A45 #93B52 #93D10 #94C05 (Secondary) #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Functional Analysis (math.FA) #Optimization and Control (math.OC) #math.FA #math.OC #msc:15A45 #msc:15B48 #msc:26C15 #msc:47L07 #msc:93B15 #msc:93B52 #msc:93D10 #msc:94C05

paper · pdf · doi:10.48550/arxiv.1202.1099

arxiv created 2012/02/06 · openalex publication_date 2012/02/06 · arxiv updated 2012/02/07 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28

Abstract

We here specialize the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued rational functions, (i) generalized positive even and (ii) odd. On the way we characterize the (non) minimality of realization of arbitrary systems through (i) the corresponding state matrix and (ii) moving the poles by applying static output feedback. We then explore the application of static output feedback to both generalized positive even and to odd functions.

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