Recently, many studies on vibration control using active suspension systems or semi-active suspension systems to decrease the lateral vibration of high speed railway vehicles have been carried out. There are many ways to solve the active suspension control problem, but if the actual plant differs from the plant that was used for the controller design to a large extent, the controller may not work well. Railway vehicles always have parameter variations in the plant, for example, vehicle body weight is varied by the number of passengers or the amount of baggage. And generally, a controller is designed assuming a reduced order model of the actual plant. Therefore there will always be a modeling error in the model that is used for the controller design. It is desired to design a robust control system which is stable for modeling error and parameter variation. In this study, computer simulation is carried out to compare the effects of using H∞ control theory, which has the advantage when modeling error and parameter variations play an important role on the system response, to the effects of using LQ control theory, which is especially useful for designing controllers, for an active suspension system or a semi-active suspension system. In addition, the effect that these suspension systems have on ride quality and running stability is examined.