This paper deals with the controller design for lateral string stabilization and vehicle following in connected vehicles with time-varying longitude velocity. The platoon of the vehicles is modeled based on LPV systems by considering the longitude velocity as scheduling parameter. To derive results less conservative than existing methods, polynomial functions are suggested to approximate various nonlinear functions of the scheduling parameter in the lateral dynamics. Approximation errors are considered as bounded uncertain parameters. Moreover, H∞ gain-scheduling dynamic output controller is designed by defining appropriate weighting functions and considering uncertain parameters in order to suppress the disturbances along the platoon. Towards this, new change of variables is proposed to derive sufficient conditions that guarantee H∞ performance in the form of parameter-dependent Linear Matrix Inequalities (LMIs). Since the measurements are available in sampling times and are transmitted through network with delay or packet dropouts, new method is proposed to determine the maximum sampling interval that guarantee the stability of the closed-loop LPV system. This method is derived based on modeling sampling process by delay operator with bounded L2 gain. The performance of the proposed gain-scheduling controller is investigated by numerical simulations. By considering real situations in which velocity in the longitude direction is variable in time, the prosperity of the proposed controller for tracking the proceeding vehicle in the platoon and attenuating of disturbances is validated.