This paper proposes a new approach to cope with the kinematic nonlinearity in the vehicle path-tracking controller synthesis problem. The kinematic nonlinearity presented in the vehicle lateral error state is found to satisfy the sector-bound condition. By isolating the sector-bounded nonlinearity via an upper linear fractional transformation (LFT), a Lur'e system is formulated. A nominal robust controller is synthesized to meet both the Popov- criterion and the regional pole placement requirement. A polytopic gain-scheduling technique is subsequently employed to accommodate the effect of the varying vehicle longitudinal velocity. Finally, an instant-turning maneuver and a sharp lane-changing maneuver are tested in carsim-simulink joint simulations whose results demonstrate the superiority of the proposed Popov- controller over a conventional controller.