Efficient slip and slide control systems are crucial in railway transportation since maximization of adhesion utilization and minimization of operating costs mainly depend on performance of such control systems. In order to improve adhesion characteristics, slip and slide control systems should hold the slip ratio at its optimum value which is determined considering vehicle velocity and environmental conditions. On the other hand, calculation of slip ratio with high accuracy is a quite challenging problem because of the difficulties in obtaining vehicle longitudinal velocity. This article proposes a novel method for robust estimation of railway vehicle velocity which uses only the angular velocity of the wheels. To this end, linear matrix inequality (LMI) approach is used to synthesize a robust estimator established on a longitudinal vehicle model with dynamic friction properties. The developed estimator is tested for extreme scenarios and the results are discussed regarding the international standards for vehicle velocity measurement in slip/slide control systems. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.