Gramian Preserving Moment Matching for Linear Systems

Time-domain moment matching-based model order reduction is an efficient technique that provides a family of parametrized reduced order models with identical moments evaluated in a set of points. The free parameters provide flexibility to impose additional constraints such as stability, passivity, and derivative matching. In this paper, for a single-input and single-output linear time-invariant system, we consider the problem of constructing a reduced-order model by balanced truncation via moment matching. We show that there exists an exo-system yielding a reduced order model with a desired controllability Gramian. Similarly, an exo-system of dual moment matching provides a reduced order model with a desired observability Gramian. Therefore, combining the two moment matching methods can yield a reduced order model by balanced truncation, opening a door to achieve model reduction by balanced truncation via moment matching