"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 p 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 p synthesis techniques are no longer adequate. In this paper we develop a procedure to tackle the mixed (real and complex) p synthesis problem. This procedure involves a "D,G-I< iteration" between computing the mixed p upper bound and solving an ' J-t, 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 p synthesis designs.