Fixed-structure LPV-IO controllers: An implicit representation based approach

In this note, novel linear matrix inequality (LMI) analysis conditions for the stability of linear parameter-varying (LPV) systems in input–output (IO) representation form are proposed together with bilinear matrix inequality (BMI) conditions for fixed-structure LPV-IO controller synthesis. Both the LPV-IO plant model and the controller are assumed to depend affinely and statically on the scheduling variables. By using an implicit representation of the plant and the controller interaction, an exact representation of the closed-loop behavior with affine dependence on the scheduling variables is achieved. This representation allows to apply Finsler's Lemma for deriving exact stability as well as exact quadratic performance conditions. A DK-iteration based solution is carried out to synthesize the controller. The main results are illustrated by a numerical example.