Positive realizations of nonlinear input-output discrete-time systems

The problem of realization of a positive nonlinear input-output discrete-time system as a positive state-space system is investigated. The input-output system is given by a difference equation of a higher order. A necessary and sufficient condition for existence of positive and regularly positively observable realization is provided. The state space variables of the realization are found as independent generators of some positive universe associated to the input-output system. Only the single-input single-output case is studied and all functions describing the systems and their properties are assumed to be continuous.