A spectral factorization method with applications to the linear-quadratic problem

This paper describes a factorization method for the solution of the LQ problem, using the work of Davis and Barry as a starting point. The factorization problem is solved by applying the reduction method to a functional equation in the Hardy space. If a Laguerre basis is used in the reduction, there results a set of block Toeplitz linear equations. The rate of decay of the error is studied. The Davis and Barry formula is extended in such a way as to enable the use of a stabilizing gain as a preliminary step.