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 recent results on bilinear matrix inequalities, this geometric interpretation allows to state the equivalence between robust controller design and the concave minimization problem.