Design of an gain scheduling state derivative feedback controller for linear parameter-varying systems

Abstract

This paper is devoted to the guaranteed cost (Formula presented.) of continuous-time linear parameter-varying (LPV) systems, considering the gain scheduling (GS) strategy and the state derivative feedback (SDF). The main contribution of the paper is to derive linear matrix inequalities (LMIs) conditions for the (Formula presented.) -SDF problem for LPV systems, taking into account the GS controller. For the good behaviour of the controller, we assume that the time-varying parameters are available for online measurement. In some cases, the (Formula presented.) -GS-SDF controller obtained high control signals, and as we intend to apply the proposed method in practical situations, we introduce the concept of (Formula presented.) -stability in the problem approach. Examples and a practical implementation show that the proposed conditions achieved good results in reducing the disturbance effect in the system. Furthermore, with the proposed methods, it is possible to guarantee the asymptotic stability and guaranteed cost (Formula presented.) minimisation.