On the formulation and solution of robust performance problems

A new approach to robust performance problems is proposed in this paper. Theapproach involves the optimisation of so-called performance weights subject to aconstraint, formulated in terms of the structured singular value, which ensures theexistence of a stabilising feedback compensator that achieves robust performancewith respect to the optimised performance weights and an uncertain plant set. Op-timising over the performance weights in this way gives rise to an algorithm forsystematically trading-off desired performance against specified plant uncertaintyand performance limitations due to plant dynamics. The algorithm also yields arobust controller. The designer is only required to specify the uncertain plant setand an optimisation directionality, which is used to reflect desired closed-loop per-formance over frequency in terms of a corresponding cost function. Design of thisdirectionality appears to be simpler than designing the performance weights directly.