This paper presents the design of a phase-based robust oscillator for wearable robots that assists the human performing periodic or repetitive tasks. The robustness of the phase oscillator controller is evaluated by finding bounds for perturbations that guaranteed the stability of the output. Then, the Lyapunov redesign method is applied to construct a robust controller using a bounding function which can handle the uncertainties such as noise and perturbations in the overall human-robot system. The robust controller produces a bounded control signal to modify the amplitude and frequency of the resulting second-order oscillator to modulate the stiffness and damping properties. In this paper, the focus is put on the wearable robot that assists human hip joint while performing periodic activities such as walking. The proposed approach is verified through a simple pendulum experiment. The results show that a better limit cycle can be obtained with Lyapunov redesigned phase oscillator which controls the radial spread of the steady state. Finally, the potential of the proposed approach for hip assistance in a healthy subject wearing HeSa (Hip Exoskeleton for Superior Assistance) during periodic activities are discussed.