Time-Domain Moment Matching for Second-Order Systems

This paper studies a structure-preserving model reduction problem for large-scale second-order dynamical systems via the framework of time-domain moment matching. The moments of a second-order system are interpreted as the solutions of second-order Sylvester equations, which leads to families of parameterized second-order reduced models that match the moments of an original second-order system at selected interpolation points. Based on this, a two-sided moment matching problem is addressed, providing a unique second-order reduced system that match two distinct sets interpolation points. Furthermore, we also construct the reduced second-order systems that matches the moments of both zero and first order derivative of the original second-order system. Finally, the Loewner framework is extended to the second-order systems, where two parameterized families of models are presented that retain the second-order structure and interpolate sets of tangential data.