<p>In this paper, two open problems of the existing bounded UDE-based robust control method are investigated: the input constraint with multiple control inputs, and the performance degradation caused by the introduced additional time-varying control variable. A modified bounded UDE-based robust control method is developed for the MIMO system with the inputs constrained by a general positive defined matrix, which is a more general condition of the norm constraint for control inputs. A nonlinear designed is further proposed to modified the direct multiplication of the additional time-varying variable to mitigate the performance degradation of the existing bounded UDE-based robust control, and the guidance of the nonlinear design procedures is provided. The proposed design is applied to the vector control of a PMSM drive system, and the simulation studies are provided to validate the proposed design under voltage constraint of the vector control with both normal operation and voltage constraint triggered.</p>