Based on the state space model of the flexible linkage mechanism equipped with piezoelectric films, a robust control methodology for suppressing elastodynamic responses of the high-speed flexible linkage mechanism with linear time-varying parameter perturbations by employing an observer-based feedback controller is presented. The instability caused by the linear time-varying parameter perturbations and the instability caused by the combined effect of control and observation spillover are investigated and carefully prevented by two robust stability criteria proposed in this paper. Numerical simulation of a slider - crank mechanism example is performed to evaluate the improvement of the elastodynamic responses.