Robust stabilization in the gap metric: controller design for distributed plants

Consideration is given to the problem of computing a controller that is optimally robust with respect to the gap ball uncertainty of a nominal infinite-dimensional plant. A technique is outlined that allows the computation of the optimal robustness radius and the corresponding controller. This theory is applied to a first-order delay system. For this system, the optimal robustness margin is computed explicitly as the solution of a certain transcendental equation. A closed-form expression for the optimal controller is given.