Factorization of positive real rational matrix functions

Abstract

This chapter is concerned with canonical factorization (with respect to the real line) of rational matrix functions with a positive definite real part on the real line. Also the generalization to pseudo-canonical factorization for functions that have a nonnegative real part is developed. All factorizations are obtained explicitly using state space realizations of the functions involved. In Section 15.1 rational matrix functions that have a positive definite real part or a nonnegative real part on the real line are characterized in terms of realizations. Section 15.2 deals with canonical factorization, and Section 15.3, the final section of the chapter, with pseudo-canonical factorization.