The general inner-outer factorization problem for discrete-time systems

In this paper we give a theoretical and a computational solution to the most general inner-outer factorization problem formulated for a discrete-time system G. Our method is based on descriptor state-space computations and relies on an efficient dislocation of the minimal indices and of the “unstable” zeros of G by left multiplication with all-pass factors. The minimal indices are dislocated by solving for the stabilizing solution an algebraic Riccati equation of order nℓ (the sum of left minimal indices) while the nb unstable zeros are dislocated by solving a Lyapunov equation of order nb. The results reported here are a non-trivial extension of a recently developed approach to the continuous-time inner-outer factorization problem.