In this paper, a Lyapunov-based synthesis of a PI-like controller is proposed for robust trajectory tracking of an independently driven and steered four-wheel mobile robot. For the robot considered in this work, an explicit structurally verified mathematical model is used to enable systematic controller design with rigorous stability guarantees suitable for real time implementation. An augmented Lyapunov-based practical stability analysis is developed for the combined velocity-error and integral-error dynamics of the inner loop, yielding explicit bounds and sufficient conditions for practical stability and uniform ultimate boundedness of the combined velocity-error and integral-error state. The resulting control law retains a PI-like structure with model-based feedforward compensation, making it suitable for implementation on standard embedded platforms while improving robustness against configuration dependent residual dynamics and unmodelled effects. The effectiveness and robustness of the proposed design are demonstrated experimentally on a four-wheel independently steered and independently driven mobile robot platform, under both horizontal and vertical operating conditions and benchmarked against a PI controller and a sliding-mode controller.