A Spectral Factorization Approach to the Distributed Stable Regular Problem; the Algebraic Riccati Equation

This paper is a study of the discrete-time infinite-dimensional “stable regulator problem” having a cost function which is not necessarily positive. We take a spectral factorization approach to the problem. Also there are results on the algebraic Riccatic equation which are equivalent to results about fixed points for a broad class of symplectic maps.