Suboptimal norm based robust control of constrained systems with an H∞ cost

The authors propose a framework that takes explicitly into account both time-domain constraints and model uncertainty. They propose an approach to time-domain constraints using an operator norm induced by the constraints to assess the stability properties of a family of systems. Specifically, they introduce a robustness measure that indicates how well the family of systems under consideration satisfies a given set of constraints. They propose a synthesis procedure based upon maximization of this robustness measure over the set of internally stable plants that satisfy additional frequency-domain specifications. The resulting optimization problem is exactly solved using a two-step approach based upon solving a constrained finite-dimensional convex optimization problem, followed by the solution of an unconstrained Nehari approximation problem. An example shows that the technique yields significant improvement over a maximum-robustness-type design