Abstract: This paper studies the problem of poles assignment constrained by mixed H₂/H_∞ performances for discrete systems. First, this problem is converted into the problem of H₂ optimization constrained by H_∞ performance and poles'location. Then an auxiliary performnce function is introduced to replace the former problem by the problem of minimization of the auxiliary performance. At last this problem is solved by Lagrange multipliers, and the static output feedback and state feedback controllers are desisned.