Guaranteed multi-loop stability margins and the gap metric

The gap metric and nu-gap metric have many appealing properties for assessing the uncertainty in a plant in a feedback configuration. This short paper addresses the question of relating these generalised stability margins to more traditional single-loop and multiloop robustness measures. In particular we show that when a system is controlled by a controller which provides a stability margin of ε in the gap metric for the weighted plant then if the weighting matrices are diagonal the plant will have robust stability to easily interpreted simultaneous gain and phase variations at all the inputs and outputs