Structural properties necessary to guarantee the existence of a stabilizing feedback control law for systems described by a set of linear time-invariant differential equations with bounded but unknown time-varying uncertanties are investigated. A monotone mapping theorem is used to explore the relation between an optimal regulator problem with and without uncertainty, and a set of generalized matching conditions are presented which insure that stabilizing feedback gains can be found. Finally, a numerically stable algorithm is presented for computing the generalized matching conditions.