This paper addresses the L-2 gain control problem for disturbance attenuation in Linear Parameter Varying (LP 11,1 Systems having sat:muting 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.