Adapting state-space reduction techniques to match steady-state responses

Many popular model-reduction techniques do not ensure matching the steady-state response of the original system to canonical inputs (harmonic and singularity inputs). This paper shows that steady-state response retention can simply be achieved by decomposing the forced response into a transient and a steady-state component and by applying the reduction method only to the first, which also ensures that the transient term is optimal with respect to the chosen criterion. The suggested reduction procedure refers to state-space representations which are often the only available when the systems to be reduced are of very high order (so that the computation of their transfer functions is not reliable). To this purpose, the aforementioned components of the forced response are expressed directly in terms of the original state-space representation. Two benchmark examples of very high dimensions are worked out to show that the performance of the resulting reduced-order models compares favourably with the performance of the models of the same order determined in the usual way, i.e., without explicit consideration of their steady-state response. © 2016 IEEE.