離散時間多項式行列のＪスペクトル分解アルゴリズム―二変数多項式行列とリカッチ方程式による解法

Abstract

This paper addresses an algorithm of J spectral factorization for discrete time polynomial matrices. Particularly, we focus on the computation of J spectral factorization for discrete time polynomial matrices. Our approach is based on two-variable polynomial matrices, which is introduced for the analysis and synthesis of discrete time dissipativeness by authors, and algebraic Riccati equations. We show that the solvablity of J spectral factorization of a given polynomial matrix is equivalent to that of an algebraic Riccati equation consisting of the coefficient matrices of the given polynomial matrix. And then we provide an algorithm of discrete time J spectral factorization. Moreover, we give an illustrative example in order to show the validity of our results.