Ellipsoid based L_2 controller design for LPV systems with saturating actuators

Abstract

This paper addresses the L_2 gain control problem for disturbance attenuation in Linear Parameter Varying (LPV) Systems having saturating actuators when the system is subjected to L_2 disturbances. In the presented method, saturating actuator is expressed analytically with a convex hull of some linear feedback which let us construct L_2 control problem via Linear Matrix Inequalities (LMIs) which are obtained by some ellipsoids. It is shown that the stability and disturbance rejection capabilities of the control system are all measured by means of these nested ellipsoids where the inner ellipsoid covers the initial conditions for states whereas the outer ellipsoid designates the L_2 gain of the system. It is shown that the performance of the controller is highly related by the topology of these ellipsoids. Finally, the efficiency of the proposed method is successfully demonstrated through simulation studies on a single-track vehicle dynamics having some linear time-varying parameters.