Controller Design with Real Parametric

A number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty. In particular the complex synthesis procedure has been successfully applied to a number of engineering problems. However the presence of real parametric uncertainty in the problem description substantially complicates matters, so that standard complex synthesis techniques are no longer adequate. In this paper we develop a procedure to tackle the mixed (real and complex) synthesis problem. This procedure involves a \D,G-K iteration" between computing the mixed upper bound and solving an H 1 optimal control problem, and has guaranteed convergence to a local minimum of the (nonconvex) problem. The procedure has been implemented in software, and several controller designs are compared with the corresponding complex synthesis designs.