Abstract: In this paper, two universal generalized minimum-variance self-tuning controllers are presented for the control of arbitrary-dimension in put arbitrary-dimension output (ADIADO) systems. These new controllers have solved the long-lasting self-tuning control problems of the following systems, to which all the existing multivariable generalized minimum variance controllers are inapplicable; (1)the dimension of input is unequal to that of output; (2)Bo is singular. Several typical simulation examples are presented to demonstrate the universality and effectiveness of these controllers.