Passive Linear Discrete-Time Systems -- Characterization through Structure

Izchak Lewkowicz

Published 2020-02-16Version 1

We here show that discrete-time passive linear systems are intimately linked to the structure of maximal, matrix-convex sets, closed under multiplication among their 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 associated structure is if of maximal matrix-convex, cones, closed under inversion.