Passive Linear Discrete-Time Systems: Characterization through Structure

2020/02/16 by Izchak Lewkowicz, Lewkowicz, Izchak
Mathematics · #15A60 26C15 47L07 47A56 47N70 93B15 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #math.FA #math.OC #msc:15A60 #msc:26C15 #msc:47A56 #msc:47L07 #msc:47N70 #msc:93B15

paper · pdf · doi:10.48550/arxiv.2002.06632

arxiv created 2021/02/02 · arxiv updated 2021/02/03

Abstract

We here show that the family of finite-dimensional, discrete-time, passive, linear time-invariant systems can be characterized through the structure of maximal, matrix-convex set, closed under multiplication among its elements. Moreover, this observation unifies three setups: (i) difference inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the continuous-time case, the corresponding structure is of a maximal matrix-convex, cone, closed under inversion.

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