Exact Order Reduction for the Fornasini-Marchesini State-Space Model Based on Common Invariant Subspace

In this paper, a new exact order reduction approach for Fornasini-Marchesini state-space models will be proposed based on common invariant subspace. It will be shown that this new approach can be applied even to those systems for which the existing approach based on eigenvalues cannot do any further exact order reduction on them. As a consequence, the approach based on eigenvalues can be viewed as a special case of the new proposed approach. Examples will be given to show the effectiveness as well as the details of the proposed approach.