A Connection Between Time Domain Model Order Reduction and Moment Matching for LTI Systems
Provides a theoretical link between two MOR techniques for LTI systems, clarifying limitations of the time-domain approach for researchers in model reduction.
The paper extends a time-domain model order reduction method using general orthogonal polynomials, showing its connection to moment matching via a Sylvester equation. Numerical examples illustrate that the time-domain approach is at best as accurate as moment matching due to fixed expansion points.
We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen 2012 and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying an equivalent Sylvester equation, we show a connection to a rational Krylov subspace, and thus to moment matching. This theoretical link between the MOR techniques is illustrated by three numerical examples. For linear time-invariant systems, the link also motivates that the time domain approach can be at best as accurate as moment matching, since the expansion points are fixed by the choice of the polynomial basis, while in moment matching they can be adapted to the system.