Passive Linear Continuous-Time Systems: Characterization Through Structure
Izchak Lewkowicz
TL;DR
This paper characterizes continuous-time linear systems using maximal matrix-convex cones closed under inversion, unifying differential inclusions, rational functions, and realization arrays, and compares with discrete-time structures.
Contribution
It introduces a unifying structural framework for continuous-time linear systems via maximal matrix-convex cones, linking various system representations.
Findings
Continuous-time systems characterized by maximal matrix-convex cones.
Unified framework encompasses differential inclusions and rational functions.
Discrete-time case involves maximal matrix-convex sets closed under multiplication.
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
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