The printing quality delivered by a Drop-on-Demand (DoD) inkjet printhead is mainly limited due to operational issues of the residual oscillations in the ink channel. The maximal jetting frequency of a DoD inkjet printhead can be increased by quickly damping the residual oscillations and by bringing in this way the ink-channel to rest after jetting the ink drop. The inkjet channel model obtained is generally subjected to parametric uncertainty. This paper proposes a robust optimization-based method to design the input actuation waveform for the piezo actuator in order to improve the damping of the residual oscillations in presence of the parametric uncertainties in the ink-channel model. Experimental results are presented to show the efficacy of the proposed method.