  We use a non-smooth trust-region method for $H_\infty$-control of
infinite-dimensional systems. Our method applies in particular to distributed
and boundary control of partial differential equations. It is computationally
attractive as it avoids the use of system reduction or identification. For
illustration the method is applied to control a reaction-convection-diffusion
system, a Van de Vusse reactor, and to a cavity flow control problem.
