Model reduction based on regional pole and covariance equivalent realizations

In this paper a novel model reduction problem is studied for linear continu ous-time time-invariant stochastic systems. The purpose of this problem is to design the reduced-order model so that it has the same dominant pole reg ion and steady-state output covariance as those of the original full-order model. The resulting reduced-order model can approximate the corresponding original full-order model in two important aspects, i.e., transient and ste ady-state performances. Necessary and sufficient and conditions for the exi stence of desired reduced-order models are established, and an explicit exp ression for these reduced-order models is also presented. An illustrative e xample is used to demonstrate the effectiveness of the proposed design meth od.