This paper presents a method for the control design of a two degrees of freedom (2-DoF) serial manipulator using descriptor Takagi-Sugeno modelling. The design goal is to achieve a guaranteed $\mathcal{H}_{\infty}$ model reference tracking performance while significantly reducing the numerical complexity of the designed controller through a robust control scheme. Based on Lyapunov stability theory, the control design is formulated as an LMI (linear matrix inequality) optimization problem. Simulation results carried out with the SimMechanics environment clearly demonstrate the effectiveness of the proposed method.