  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.
