9 - A refined resolvent decomposition of a regular polynomial matrix and application to the solution of regular PMDs

Abstract

This chapter presents a resolvent decomposition which is a refinement of the state-of-the-art results. It is formulated in terms of the notions of the finite Jordan pairs, infinite Jordan pairs, and the generalized infinite Jordan pairs. We make clear the issue of infinite Jordan pair noted by a number of references. This refined resolvent decomposition captures the essential feature of the system structure. Further, the redundant information, which is included in the known resolvent decomposition, is deleted through a certain transformation, thus the resulting resolvent decomposition inherits the advantages of the reported results. This refined resolvent decomposition facilitates computation of the inverse matrix of A(s) due to the fact that the dimensions of the matrices used are of minimal.