Order reduction of SISO nonminimum phase stochastic systems

We consider the order reduction problem for single-input/single-output nonminimum-phase linear stochastic systems. The problem is formulated as that of approximating the original system-output process by another stochastic process generated via a reduced-order model. It is shown that in order to obtain a "correct" phase approximation, it is necessary to consider some higher-order statistics of the original process in addition to the usual second-order statistics. A computationally feasible approximation criterion is proposed and analyzed. An example is also presented to illustrate the proposed method.