Reduced-order local representation of uncertain large-scale interconnected systems

We address the structure-preserving model reduction problem of uncertain large-scale systems. The uncertainties under consideration include local uncertainty and interconnection uncertainty, both of which are modeled in terms of IQCs. The performance of the reduced-order system is justified in H_∞ sense. It is shown that the feasibility of a collection of rank constrained LMIs is both sufficient and necessary for the existence of a reduced-order representation of the original system. A guaranteed upper bound on the worst-case model reduction performance is also obtained. To obtain a reduced-order model satisfying this bound, related optimization problems involving rank constrained LMIs are discussed.