A Calculation of Minimal Basis in Polynomial Vector Space with Applications

Abstract

Given a transfer function matrix N(s)D^-1(s), the problem discussed in this paper is to find an orthogonal matrix pair [N(s)-D(s)] to [D^T(s) N^T (s)]^T. A calculation method of the orthogonal pair is presented where only elementary real matrices operation needs. It is shown that an annihilating matrix of an observability matrix of N(s)D^-1(s) provides the orthogonal pair. Some related problems in linear system theory are also discussed.