Moment matching for second-order systems with pole-zero placement

In this paper, a structure-preserving model reduction problem for second-order dynamical systems of high dimension using time-domain moment matching with pole-zero placement is studied. The moments of a second-order system are defined based on the solutions of linear matrix equations. Families of second-order reduced models, parameterized in a set of matrix degrees of freedom, that match the moments of a given second-order system at selected interpolation points are computed. We then provide formulae for the set of matrix parameters such that the reduced order approximation has a set of prescribed poles and zeros. The theory is illustrated on a damped vibratory system (e.g., a chain of mechanical oscillators) of degree n, governed by a second-order dynamical model.