Controller synthesis for input-output LPV models

This paper considers the synthesis of linear parameter-varying (LPV) controllers for plant models given in input-output LPV form. For SISO systems, a method for synthesizing LPV gain-scheduled controllers in input-output form has been proposed recently, where the a priori choice of a central polynomial plays a critical role, and the synthesis problem is solved using a sum-of-squares relaxation. In this paper we propose a way of simplifying this design procedure, by replacing the sum-of-squares approach by representing the closed-loop model in polytopic input-output LPV form and then using a gradient-based optimization to solve the synthesis BMI. In this procedure the central polynomial is tuned while the closed-loop performance index is minimized over the decision variables, which include the controller parameters. The proposed method is illustrated with simulation examples.