Optimal robustness in the gap metric

The application of the gap metric to robust stabilization of feedback systems is considered. In particular, a solution to the problem of robustness optimization in the gap metric is presented. The problem of robust stabilization under simultaneous plant-controller perturbations is addressed, and the least amount of combined plant-controller uncertainty, measured by the gap metric, that can cause instability of a nominally stable feedback system is determined. Included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the T-gap metric. A key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations. This settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well-defined metric