Two-Sided Time-Domain Moment Matching for Linear Systems

In this technical note we study the problem of computing reduced order models of order ν that match 2ν moments of the given to-be-reduced system at two sets of ν interpolation points, called two-sided moment matching, in the time-domain framework. We also study the time-domain moment matching problem of the state-space representations of the first order derivative of a transfer function. Based on this, we show that the solution of the two-sided time-domain moment matching problem at non-distinct (ν) interpolation points yields a unique ν order model that satisfies the following properties: the model matches the moments of the given system at the interpolation points and the same property holds for the first order derivatives of the corresponding transfer functions.