Closed-Loop Model Reduction by Moment Matching for Linear Systems

We study the model reduction by moment matching problem for linear systems in a closed-loop configuration. First we show that the moments of a linear system can be expressed in a form that is independent of the structure of the signal generator. Then we define a class of reduced-order models that can replicate the steady-state response of the original system from input-output data. Finally, we demonstrate the applicability of the results using two simple numerical examples.