H-infinity optimal control for infinite-dimensional systems with strictly negative generator

A simple form for the optimal H-infinity state feedback of linear time-invariant infinite-dimensional systems is derived. It is applicable to systems with bounded input and output operators and a closed, densely defined, self-adjoint and strictly negative state operator. However, unlike other state-space algorithms, the optimal control is calculated in one step. Furthermore, a closed-form expression for the L2-gain of the closed-loop system is obtained. The result is an extension of the finite-dimensional case, derived by the first two authors. Examples demonstrate the simplicity of synthesis as well as the performance of the control law.