Factorizations of Transfer Functions
Harm Bart, Israel Gohberg, M. A. Kaashoek, Paul Van Dooren · SIAM Journal on Control and Optimization · 1980
This paper is concerned with minimal factorizations of rational matrix functions. The treatment is based on a new geometrical principle. In fact, it is shown that there is a one-to-one correspondence between minimal factorizations on the one hand and certain projections on the other. Considerable attention is given to the problem of stability of a minimal factorization. Also the numerical aspects are discussed. Along the way, a stability theorem for solutions of the matrix Riccati equation is obtained.