This paper investigates an H∞ Observer-Based Controller design for tracking a tramway system eco-driving trajectory. The model of the tramway system is given in state space form, and the poor manoeuvres of the of the driver when following a reference trajectory are modeled as disturbances with finite energy that affect the system dynamics. To minimize the impact of poor driver manoeuvres, an H∞ Observer-Based Tracking Controller (H∞-OBTC) was designed and its conditions of existence are given. In addition, to ensure the robust convergence of the estimation and the tracking errors simultaneously, a new sufficient condition was obtained based on the Bounded Real Lemma. Two algorithms are presented to solve the robust stability condition obtained. The first one is based on a two-step procedure. Then a linearization approach was used to present the robust stability condition of the errors as a convex optimization problem with a Linear Matrix Inequality (LMI) constraint. The gain matrices of the H∞-OBTC can be computed by solving the LMI given, subject to a minimization constraint.