Reduced-order H∞ filtering for stochastic systems

This paper deals with the reduced-order H_∞ filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.