In this study, an output feedback control strategy for the pneumatic asymmetric cylinder is established by integrating a robust controller with the proposed desired compensation adaptive law and extended sliding mode observer (ESMO). Specifically, in order to attenuate the parametric uncertainties, a desired compensation indirect-type estimation method, based on physical model and desired system states, is designed to achieve estimates of model parameters, and the parameter estimation error can be regarded as part of the lumped uncertainties. Since only displacement signal is available, both the unmeasured system states and lumped uncertainties are estimated by the proposed ESMO, and the global stability is guaranteed by the presented robust control law. As a result, structured (i.e., parametric uncertainties) and unstructured (i.e., lumped uncertainties such as unmodeled dynamics, external disturbance and parameter estimation error) uncertainties can be handled and compensated, respectively, in one controller. The comparative experimental results indicate that the prescribed tracking trajectory can be achieved by the proposed controller in the presence of time-varying uncertainties.