Using Implicit IO Representations for Stability Analysis and LPV-IO Controller Synthesis

In this paper, a novel model-based LPV controller synthesis approach is proposed for designing fixed-structure LPV controllers based on an input-output (IO) representation form. Both the LPV-IO LPV model and the LPV-IO controller are assumed to depend affinely and statically on the scheduling variables. By using an implicit representation of the system model and the controller, an exact representation of the closed-loop behavior with affine dependency on the scheduling variables is achieved. This representation allows to apply Finsler’s Lemma for deriving novel stability as well as quadratic performance conditions in the form of bilinear matrix inequalities (BMIs).