Robustness Optimization for Abstract, Uncertain Control Systems: Unbounded Inputs and Perturbations

Abstract Recently, considerable interest has been shown in various state space approaches to the robustness optimisation for linear systems. In this paper we address the problem of robustness optimisation for infinite dimensional systems with respect to a class of bounded feedback control laws, but allow both unbounded inputs and perturbations. Solution of the problem is via a doubly parameterised weak algebraic Riccati equation. Well-posedness of the abstract control system and perturbation problem is guaranteed by specifying Pritchard Salamon type conditions on the system parameters.