Controller design with real parametric uncertainty

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 μ synthesis procedure has been successfully applied to a number of engineering problems. However, the presence of real parametric uncertainty in the problem substantially complicates matters, so that standard complex μ synthesis techniques are no longer adequate. This paper develops a procedure to tackle the mixed (real and complex) μ synthesis problem. This procedure involves a (D, G)-K iteration between computing the mixed μ upper bound and solving an H ∞ optimal control problem. The resulting scheme has guaranteed convergence, though not necessarily to the global optimum of the (non-convex) problem. The (D, G)-K iteration has been implemented in software, and several controller designs are carried out and compared with the corresponding complex μ synthesis designs, to illustrate the advantages of the new technique.