A discrete stability equation theorem and method of stable model reduction

A method to derive stable reduced-order models for a stable discrete-time invariant system is presented. The method is based on a unit circle stability criterion. This criterion is the r-plane equivalent of a stability criterion for continuous time systems and is proven by using the bilinear transformation. The resulting model reduction method forms the discrete analogue of the stability equation and Michailov's methods for the simplification of continous time systems, that were recently suggested in various, closely related, versions.