The Weighted Gap Metric and Structured Uncertainty

We consider the problem of achieving robust stability in the face of input and output multiplicative uncertainties and show how it is related to the problem of achieving robust stability in the gap metric. The problem of robustness in the weighted gap metric is then addressed and it is shown how we may design against structured uncertainty by an appropriate choice of weights. The problem of optimal weighted gap robustness is formulated. This problem can be solved approximately using Doyle's D-K iteration.