A Parametric Class of Zero Locations for Stochastic Model Reduction

Recent approaches to stochastic model reduction have followed the balancing approach introduced by Moore for the deterministic model reduction problem [1]. In this approach, a given model is transformed to one in which the state variables are ordered with respect to their contribution to some criterion, and the reduced-order model is then obtained by deleting the least important variables. In the stochastic case, there is some flexibility in choosing the zeros of the reduced-order model, although the pole locations are fixed by the balancing procedure. Two choices of zero locations have been given in the literature, but the question of which one is "best" seems to be problem dependent. In this paper, it is shown that a parametric class of zero locations can be defined which includes the two choices given previously. By finding the optimum parameter values, the best set of zero locations from this class can be determined.