Revisiting and generalizing the dual iteration for static and robust output-feedback synthesis

The dual iteration was introduced in a conference paper in 1997 by Iwasaki as an iterative and heuristic procedure for the challenging and non-convex design of static output-feedback controllers. We recall in detail its essential ingredients and go beyond the work of Iwasaki by demonstrating that the framework of linear fractional representations allows for a seamless extension of the dual iteration to output-feedback designs of practical relevance, such as the design of robust or robust gain-scheduled controllers. In the paper of Iwasaki, the dual iteration is solely based on, and motivated by algebraic manipulations resulting from the elimination lemma. We provide a novel control theoretic interpretation of the individual steps, which paves the way for further generalizations of the powerful scheme to situations where the elimination lemma is not applicable. As an illustration, we extend the dual iteration to a design of static output-feedback controllers with multiple objectives. We demonstrate the approach with numerous numerical examples inspired from the literature.