Model reduction for uncertain stochastic systems

The problem of robust H_∞ model reduction for uncertain stochastic systems with time-delay is considered in this paper. For a given stable system, we focus on the construction of reduced-order models which guarantee the corresponding error system to be asymptotically stable and have a prescribed H_∞ performance. Sufficient conditions are obtained for the existence of solutions to time-delay dependent problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. In addition, the development of reduced-order model with special structures, such as zeroth-order model, delay-free model, no parameter uncertainties model, are also studied. Finally, the effectiveness of the proposed model reduction method is illustrated by a numerical example.