Computation of irreducible generalized state-space realizations

In this paper, an efficient, numerically stable procedure is presented for the computation of irreducible generalized state-space realizations from non-minimal ones. The order reduction is performed by removing successively the uncontrollable and the unobservable parts of the system. Each reduction is accomplished by the same basic algorithm which deflates the uncontrollable part of the system using orthogonal similarity transformations. Applications of the proposed procedure are also presented.