Factorization of positive definite rational matrix functions

Abstract

The central theme of this chapter is the state space analysis of rational matrix functions with Hermitian values either on the real line, on the imaginary axis, or on the unit circle. The main focus will be on rational matrix functions that take positive definite values on one of these contours. It will be shown that if W is such a function, then W admits a spectral factorization, i.e., a canonical factorization W=W₋W₊ with an additional symmetry between the corresponding factors, depending on the contour.