Title: "Robust control via nonlinear optimization."

Abstract: During the last decade, interior point methods for semidefinite programming (SDP) have been one of the principal themes in nonlinear optimization. This was in large parts due to the fact that in the early ninties, a variety of problems in feedback control design could be cast as linear matrix inequality (LMI) feasibility problems, and were therefore open to new algorithmic resolution strategies. On a closer look, however, the majority of control applications may only be cast as bilinear matrix inequality (BMI) problems, and in consequence, require extensions of SDP. We discuss possible extensions, and we take a closer look at robust feedback control design, which is perhaps the most important application open to these new methods.