Robust, reduced-order modeling for state space systems via parameter-dependent bounding functions

The problem of approximating a high-order system with constant real parameter uncertainty by a reduced-order model is considered. A parameter-dependent quadratic bounding function is developed that bounds the effect of uncertain real parameters on the model-reduction error. An auxiliary minimization problem is formulated that minimizes an upper bound for the model-reduction error. The principal result is a necessary condition for solving the auxiliary minimization problem which effectively provides sufficient conditions for characterizing robust reduced-order models