Positive nonlinear realizations of response maps

The problem of realization of a positive response map as a positive initialized system on a finite dimensional Euclidean state space is investigated. The dynamical part of the system is described by a delta differential equation on an arbitrary time scale. This incorporates continuous- and discrete-time systems. The main result states necessary and sufficient conditions for existence of positive realization of a particular class. The criterion is expressed in the language of skew differential global universes.