Since there is a coupling between lateral and vertical dynamics, the interactions between control components must be taken into consideration. The paper presents the effects of vertical load variations on the controlled invariant set of the steering system. In the model the nonlinear characteristics of the tire force are approximated by the polynomial form. The analysis is based on Sum-of-Squares programming method and parameter-dependent polynomial control Lyapunov functions. The Maximum Controlled Invariant Sets of the steering as a function of vertical loads are illustrated through a simulation example. The results of the analysis are built into the control design of the suspension system. A semi-active suspension system using preview control is applied. The operation of the controller is illustrated through simulation examples.