Guaranteed accuracy computations in systems and control

This paper is concerned with the problem of validation in the context of numerical computations in control. We explore the possibility of using computer algebra tools and interval methods to compute solutions which have guarantees on accuracy, e.g. which are not subject to unknown errors due to rounding or approximation. We demonstrate that this is possible for two common norms of a linear system (L2 and L∞) and H2-optimal controller synthesis. We further discuss some of the issues involved in achieving a validation property for other problems of controller synthesis.