The research extended the newly developed Critical Direction Theory. Given general uncertainties from modeling error or practical implementation inaccuracy, this theory helps to identify the critical components that are of relevance to stability analysis and disregard all other irrelevant uncertain parts.

We explored advantages of this theory over other existing approaches for robustness analysis of systems with parameters having uncertain complex or real values, and solved for the maximum stability margin in an exact manner. Our research on robustness analysis provided not only real ? and mixed ? analysis methods, but also established a sound foundation for robustness synthesis research.

We finally tackled robustness synthesis problems, and constructed a robust controller design methodology which combined the essence of the new theory and H8 design. An important attempt reported in literature on robust controller design was to use standard H8 design while replacing a family of uncertainties with the maximum uncertainty value. We exposed the mechanism leading to conservatism of this over-bounding operation according to the principle of the critical direction theory. Further research resulted in an exact representation of the family of uncertainties. The previous conservatism was dramatically reduced and a much larger allowable uncertainty size was achieved. This research equips engineers and researchers a systematic methodology to design a robust controller in an exact fashion for highly complicated uncertain systems, resulting in good performance and cost-effectiveness.