Solution to the general inner-outer and spectral factorization problems

Dr. Andras Varga, German Aerospace Center (DLR), Germany

Two related problems in linear systems theory are considered in the most general setting: the computation of the inner-outer and spectral factorizations of a continuous-time system. These factorization problems rely essentially on solving for the stabilizing solution a standard algebraic Riccati equation of order usually much smaller than the McMillan degree of the transfer function matrix of the system. The recently developed new procedures are completely general being applicable for a polynomial/proper/improper system whose transfer function matrix could be even rank deficient and could have poles/zeros on the imaginary axis or at infinity. As an application we discuss the computation of the Moore-Penrose pseudo-inverse of a rational matrix.