Algebraic approach to robust controller design: a geometric interpretation

The problem of robust controller design is addressed for a single-input single-output plant with a single uncertain parameter. Given one controller that stabilizes the nominal plant, the Youla-Kucera parametrization of all stabilizing controllers and quadratic forms over Hermite-Fujiwara matrices are used to provide clear and simple geometric answers to the following questions: Can the plant be robustly stabilized by a nominally stabilizing controller? How can this robust controller be designed? Thanks to results on bilinear matrix inequalities, this geometric interpretation allows us to state the equivalence between robust controller design and the concave minimization problem