H_∞ Model Reduction in the Stochastic Framework

This paper investigates the problems of H∞ model reduction for both continuous and discrete stochastic systems. In terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint, necessary and sufficient conditions for the existence of solutions to such problems are obtained. An explicit parametrization of all reduced-order models corresponding to a feasible solution is also proposed. In particular, when a zeroth-order H∞ approximation is desired, conditions are obtained using LMIs only without any rank constraints, and a parametrization of all solutions is also presented. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.