Cone-Realizations of Discrete-Time Systems with Delays

摘要

A new notion of cone-realization for discrete-time linear systems with delays is proposed. Necessary and sufficient conditions for the existence of cone-realizations of discrete-time linear systems with delays are established. A procedure is proposed for computation of a cone-realization for a given proper rational matrix T(z). It is shown that there exists a (P,Q,V)-cone realization of T(z) 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.