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The article deals with the technique developed for the parametric design of a robust controller which ensures the desired robust quality indicators in the system with interval parameters. This technique is based on the construction of the D-partition in the space of controller parameters at vertices of the coefficient polyhedron of a characteristic polynomial. Grounds for this are the fact that the interval system has its minimum degree of stability and maximum degree of oscillation at certain vertices of the specified polyhedron. To determine the minimum sets of those vertices, a new technique has been developed. The developed technique is based on inequalities obtained for outlet angles of the edge branches coming out from system poles, which determine the root indices of robust quality. Applying the developed technique for the vertex D-partition, the design of the PI controller of the stabilization system for a tethered underwater vehicle has been carried out. The results of the design confirm the efficiency of the developed approach.