Algebraic properties of minimal degree spectral factors

Abstract

The paper derives a result connecting frequency-domain and time-domain properties of different spectral factors of the one power spectrum matrix. These results are interpreted from an algebraic point of view, and applied to the linear-quadratic optimal control and filtering problem. Interpretations are given of the phenomenon that many optimal control problems can lead to the same optimal control law but different optimal cost, and likewise many filtering problems can lead to the same optimal filter, but different filter performance. Show more