This paper investigates the joint design of the beamforming scheme in intelligent reflecting surface (IRS) assisted multiuser (MU) multiple-input multiple-output (MIMO) downlink transmissions. Channel estimation errors associated with the minimum mean square error (MMSE) estimation are assumed and the weighted sum rate (WSR) is adopted as the performance metric. Low-resolution phase shifters (PSs) in practical implementations are taken into account as well. Under the constraint of the transmit power and discrete phase shifters (PSs), an optimization problem is formulated to maximize the WSR of all users. To obtain the optimal beamforming matrices at the IRS, two solutions based on the majorization-minimization (MM) and successive convex approximation (SCA) methods, respectively, are proposed. Through simulation results, both of the proposed two schemes achieve a significant improvement in WSR. Furthermore, the superiority of the SCA-based solution is demonstrated. Overall, two viable solutions to the joint beamforming design in IRS-aided MU-MIMO downlink communication systems with channel estimation errors are provided.