Structured H∞-control of infinite-dimensional systems

We develop a novel frequency-based H-infinity-control method for a large class of infinite-dimensional linear time-invariant systems in transfer function form. A major benefit of our approach is that reduction or identification techniques are not needed, which avoids typical distortions. Our method allows to exploit both state-space or transfer function models and input/output frequency response data when only such are available. We aim for the design of practically useful H-infinity-controllers of any convenient structure and size. We use a nonsmooth trust-region bundle method to compute arbitrarily structured locally optimal H-infinity-controllers for a frequency-sampled approximation of the underlying infinite-dimensional H-infinity-problem in such a way that (i) exponential stability in closed loop is guaranteed and that (ii) the optimal H-infinity-value of the approximation differs from the true infinite-dimensional value only by a prior user-specified tolerance. We demonstrate the versatility and practicality of our method on a variety of infinite-dimensional H-infinity-synthesis problems, including distributed and boundary control of partial differential equations, control of dead-time and delay systems, and using a rich testing set.