Model reduction based on regional pole and covariance equivalent realizations

In this paper a novel model reduction problem is studied for linear continuous-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 region 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 steady state performances. Necessary and sufficient conditions for the existence of desired reduced-order models are established, and an explicit expression for these reduced order model is also presented. An illustrative example is used to demonstrate the effectiveness of the proposed design method