<p>Microvibrations seriously impact the precision and stability of precision mechanical systems and structural components in practical engineering. In this study, a piezoelectric-actuated integrated active-passive vibration isolator (IAPVI) is investigated to suppress the vibrations. Initially, a control-oriented model for the piezoelectric-actuated IAPVI is derived through compensation and order reduction techniques. The vibrations are fully considered as matched and mismatched disturbances in the system. Subsequently, based on the obtained model, an output feedback sliding model predictive control (SMPC) method is designed for the IAPVI. In the proposed scheme, the observers are adopted to estimate the system states and disturbances. Thus, the measurement of system states is avoided. A sliding mode surface consisting of the estimated states and disturbances is designed, which enhances the ability of the proposed controller to address mismatched disturbances. Based on the principle of receding horizon optimization, the sliding mode state is predicted to track the predefined discrete reaching law. It eliminates the chattering phenomenon and enables the proposed controller to deal with constraints explicitly. The stability of the closed-loop system is analyzed, and the mismatched disturbances are proved to be mitigated in the output channel of the system. Finally, extensive experiments are conducted on the IAPVI to validate the effectiveness of the proposed scheme.</p>