Spectral factorization of non-classical information structures under feedback

We consider linear systems under feedback. We restrict our attention to non-classical information structures for which the optimal control policies can be found via a convex optimization problem. The first step to analytically solving such control problems is performing a spectral factorization to solve the optimality condition. In this paper we discuss two classes of information structures, for which such spectral factorizations can be found. In the first structure, the only constraint is that the controller can remember previous inputs that it has received. In the second structure, we consider a controller which is allowed to forget previous observations.