Optimal Popov controller analysis and synthesis for systems with real parameter uncertainties

Robust performance analysis plays an important role in the design of controllers for uncertain multivariable systems. Recent research has investigated the use of absolute stability criteria to develop less conservative analysis tests for systems with linear and nonlinear real parameter uncertainties. This note extends previous work on optimal X2 performance analysis using the Popov criterion by presenting an numerical homotopy algorithm that can be used to analyze systems with less restrictive assumptions on the structure of the uncertainty block. The technique is used to compare relative robustness capabilities of the various control algorithms that have been designed for the Middeck active control experiment (MACE). The analysis is combined with the previously presented Popov controller synthesis to yield compensators that guarantee robust performance for systems with real parameter uncertainty.