Solutions to the optimal filtering and open-loop control problems using a generalized parallel model scheme are presented. The solutions are based on the algebra of polynomial matrices. Different cases are treated such as H-2-optimal design in continuous and discrete time domain and the optimal sampled data design. The procedure is simple and involves the solution of linear matrix polynomial equations whose coefficients are obtained by spectral factorizations. The sampled data design is based on iterations which approximate the optimal solution as closely as desired.