Abstract: The problem of ■₁ optimization design for given order controller based on multiple input-multiple output（MIMO） discrete-time system is studied.Based on Youla parameterization,the free parameter Q is discussed for two cases,i.e.,polynomial and rational polynomial,and the rational case is translated into the polynomial one;eventually,the optimization problem of given order controller is transformed into solving the problem of standard linear programming.Given the controller's order,the optimal controller is obtained which enables the closed-loop system to be internally stabilized and the corresponding ■₁ norm to be minimized.Finally,an example is presented to illustrate the validity of the algorithm.