Solutions to the general inner-outer and spectral factorization problems

• Published in: Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171) Vol. 3; pp. 2774 - 2779 vol.3
• Main Authors: Oara, C., Varga, A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1998
• Subjects: Aerodynamics; Automatic control; Ear; Poles and zeros; Polynomials; Robots; Terminology
• ISBN: 9780780343948; 0780343948
• ISSN: 0191-2216
• DOI: 10.1109/CDC.1998.757875

In this paper we solve two open problems in linear system theory: the computation of the inner-outer and spectral factorizations of a descriptor continuous-time system considered in the most general setting. Our method is based on descriptor state-space computations and relies on three techniques developed for rational matrices: compression of G to a surjective (full row rank) matrix, and dislocation of the unstable zeros/poles of G to stable locations, all achieved by left multiplication with all-pass factors. The proposed procedures are completely general being applicable for G polynomial/proper/improper, of arbitrary rank, with poles/zeros on the imaginary axis.