  H-infinity optimal control and estimation are addressed for a class of
systems governed by partial differential equations with bounded input and
output operators. Diffusion equations are an important example in this class.
Explicit formulas for the optimal state feedback controller as well as the
optimal state estimator are given. Unlike traditional methods for H-infinity
synthesis, no iteration is needed to obtain the optimal solution. Moreover, the
optimal performance for both the state feedback and state estimation problems
are explicitly calculated. This is shown to be useful for problems of
H-infinity optimal actuator and sensor location. Furthermore, the results can
be used in testing and bench-marking of general purpose algorithms for
H-infinity synthesis. The results also apply to finite-dimensional systems.
