Solution to the General Inner-Outer and Spectral Factorization Problems

Abstract

In this paper we solve two open problems in linear system theory: the computation of the spectral and inner-outer factorizations of a rational matrix G in the most general setting. Our approach has also important theoretical consequences as we show that these factorization problems, even in the most general case, rely essentially only on solving for the stabilizing solution and standard algebraic Riccati equation of order nl, where nl is the sum of the left minimal indices of G and is usually smaller than the McMillan degree of G.