  The relaxation systems are an important subclass of the passive systems that
arise naturally in applications. We exploit the fact that they have highly
structured state-space realisations to derive analytical solutions to some
simple H-infinity type optimal control problems. The resulting controllers are
also relaxation systems, and often sparse. This makes them ideal candidates for
applications in large-scale problems, which we demonstrate by designing simple,
sparse, electrical circuits to optimally control large inductive networks and
to solve linear regression problems.
