The purpose of this paper is to develop an analytic way for designing optimal PI-controllers for the interval plant family. Optimality means that the coefficient intervals of the plant stabilized by a PI-controller is maximized. It will be shown that the optimization problem can be formulated in terms of an eigenvalue minimization problem of matrix pairs of the form (H(h 0, g 0), H(δ 1,κ , δ 2,κ )), where κ = 1, 2, 3, 4 and both H(h 0, g 0) and H(δ 1,κ , δ 2,κ ) are frequency independent Hurwitz-like matrices. A numerical example is provided to illustrate that optimal controller parameters can be successfully obtained by a two-dimensional search.