Model reduction via projection of generalized state space systems

We show that the projection of generalized state space models of SISO systems allows to construct arbitrary lower order models and that they can be obtained via the solution of particular generalized Sylvester equations. This generalizes the results already obtained for state space systems, where both the original models and low order models were constrained to be strictly proper. We also conjecture that for MIMO systems, this approach is as general as one can hope for.