Gradient formulations for sensitivity-based QFT performance bounds

QFT performance and stability bounds, at each frequency, can be cast as a set of circles in the complex plane, the outermost boundary of the union of this set being the resultant bound. This can be shown by the use of normalized plant uncertainty and sensitivity functions. We show that these bounds can possess a closed-form gradient expression, similar to the traditional, template-based bounds. Constrained optimization of controller parameters as previously demonstrated for the traditional problem can thus be applied