Model reduction by reproducing the asymptotic response

The forced response of a linear stable system can be decomposed into a system component (transient term), an input component (steady-state or asymptotic term) and, possibly, an interaction component (resonant term). The paper considers the problem of determining reduced-order model that reproduce the original input and interaction components for suitable inputs. The choice of the input depends on the order of the reduced model and its desired performance. The interpolation properties enjoyed by the resulting approximating transfer function are pointed out. It is shown that several popular reduction methods can be regarded as particular cases of the suggested approach. Finally, two illustrative examples are given.