Ellipsoid based L2 controller design for LPV systems with saturating actuators

This paper addresses the L2 gain control problem for disturbance attenuation in Linear Parameter Varying (LPV) Systems having saturating actuators when the system is subjected to L2 disturbances. In the presented method, saturating actuator is expressed analytically with a convex hull of some linear feedback
which let us construct L2 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 L2 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.