Abstract A 2-mass system connected by a non-ideal shaft has resonance modes, and it is difficult to design a controller suppressing the vibration in the face of parameter variation. This paper proposes a method of μ-synthesis based on the descriptor form representation to deal with parameter uncertainties independently. First, a class of parameter uncertainty given in the descriptor form is considered, and the paper shows how to achieve robust stability and robust performance for this class of perturbed systems. Then this method is applied to a 2-mass system with parameter uncertainties of the torsional constant and the load inertia. By using this method these two physical uncertainties are treated independently, and a controller is designed to achieve not only robust stability but also robust disturbance suppression. In addition, a two- degree-of-freedom control scheme is used to achieve a good transient response. Simulation results are presented to demonstrate the control effects.