Computation of realizations of discrete-time cone-systems

A new notion of a realization of transfer matrix of (P, Q, V)-cone-system for discrete-time linear systems is proposed. Necessary and sufficient conditions for the existence of the realizations are established. A procedure is proposed for computation of a realization of a given proper transfer matrix T(z) of (P, Q, V)-cone-system. It is shown that there exists a realization of T(z) of (P, Q, V)-cone-system if and only if there exists a positive realization of T(z) = VT(Z)Q-1, where V, Q and P are non-singular matrices generating the cones V, Q and P respectively.