Convex analysis of discrete-time uncertain Hinfinity control problems

Two classical problems involving discrete-time systems are analyzed. The first one concerns the quadratic stabilizability with uncertainties in convex bounded domains, which naturally covers the important class of interval matrices. In that problem, there is no need to introduce any kind of matching conditions, which is an important improvement compared with other results available in the literature. The second problem is defined by simply adding to the first problem some prespecified closed-loop transfer function H_infinity norm bound. Assuming the state is available for feedback, the geometry of both problems is thoroughly analyzed. They turn out to be convex on the parameter space.