State-response decomposition for model reduction

The decomposition of the overall forced response into a steady-state and a transient component can be exploited to find reduced-order models that retain both long-term and short-term characteristics of the original system behaviour. To this purpose, the state-space expressions of the aforementioned components in response to inputs with rational transform are derived. The reduced-order model is then obtained by considering separately the asymptotic and transient terms. The suggested approach is tested on benchmark examples of very high dimension.