Fixed-structure LPV controller synthesis based on implicit input output representations

In this paper a novel LPV controller synthesis approach to design fixed-structure LPV controllers in input output (IO) form is presented. The LPV-IO model and the LPV-IO controller are assumed to depend affinely as well as statically on the scheduling variable. By using an implicit representation of the system model and the controller, an exact representation of the closed-loop behavior is achieved. Using Finsler´s Lemma, novel stability conditions are derived in the form of linear matrix inequalities (LMIs). Based on these conditions a quadratic performance synthesis approach is introduced in form of bilinear matrix inequalities (BMIs) and solved using a DK-iteration based approach.