A real-time model-based controller is developed for the tracking of the distributed safety-factor profile in a tokamak plasma. Using relevant physical models and simplifying assumptions, theoretical stability and robustness guarantees were obtained using a Lyapunov function. This approach considers the couplings between the poloidal flux diffusion equation, the time-varying temperature profiles and an independent total plasma current control. The actuator chosen for the safety-factor profile tracking is the lower hybrid current drive, although the results presented can be easily extended to any non-inductive current source. The performance and robustness of the proposed control law is evaluated with a physics-oriented simulation code on Tore Supra experimental test cases.