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This paper addresses the problem of output feedback control design for a class of multi-input-multi-output (MIMO) nonlinear systems where the number of inputs is less than that of outputs. There are two difficulties in this design problem: (1) too few control inputs will not generally allow independent control over all outputs and (2) the state of the system is not available for measurements, and only the outputs are available through measurements. To address the first issue, a practical output feedback control problem is formulated, aiming to regulate only part of the outputs, and a controller structure with two design components in all or some chosen control inputs is proposed. To cope with the second difficulty, the recently developed high-order sliding mode differentiators (HOSMDs) are used to estimate the derivatives of the outputs needed in the controller design. With the derivatives estimated using HOSMDs, an output feedback controller is designed using the backstepping approach. Stability results are established for the designed controller under certain conditions. In order to test the applicability of the proposed output feedback controller in practical industrial problems, experiments are carried out though implementing the controller on a laboratory-scale 3-D crane. The experimental results are presented and reveal the advantage of the proposed controller structure, as well as the effect of controller gain and sampling periods.