Uncertainty in the weighted gap metric: A geometric approach

Abstract

The stability of control systems is studied in the context of weighted input-output signal spaces. Necessary and sufficient conditions for a controller to stabilize a plant are given in terms of geometric notions. These geometric quantities can be calculated by solving H ∞ optimization problems. Maximally stabilizing controllers in a weighted signal space are introduced and characterized in terms of Nehari extensions. The robustness properties of maximally stabilizing controllers are analysed in terms of weighted coprime factor uncertainty. Necessary and sufficient conditions are established for a controller of a given plant to be the maximally stabilizing controller of the plant with respect to a weight. An upper bound for the mixed-sensitivity of a control system is given where the controller is the maximally stabilizing controller of the plant.