Minimal positive continuous-time realizations of positive response maps

Abstract

Positive nonlinear continuous-time local realizations of positive response maps are studied. The realizations are minimal if they are positively reachable and positively observable. Necessary and sufficient conditions for a response map to have a minimal positive local realization are provided. It is also shown that a minimal positive local realization has the minimal dimension among all positive local realizations of the given response map and that it is unique up to an isomorphism of systems.