Moment matching with prescribed poles and zeros for infinite-dimensional systems

In this paper we approach the problem of moment matching for a class of infinite-dimensional systems, based on the unique solution of an operator Sylvester equation. It results in a class of parameterized, finite-dimensional, reduced order models that match a set of prescribed moments of the given system. We show that, by properly choosing the free parameters, additional constraints are met, e.g., pole placement, preservation of zeros. To illustrate the proposed method, we apply it to the heat equation with mixed boundary conditions. We obtain a second order reduced model which approximates the original systems better (in terms of the infinity norm of the approximation error) than the fourth order reduced model obtained by modal truncation.