Passive Linear Continuous-Time Systems: Characterization Through Structure

Abstract

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