Abstract The diagonal stabilization problem (DSP) is defined over the ring of proper rational functions which have no poles inside a prescribed region of the finite complex plane. Solvability is intimately related to systems which exhibit the property of cyclicity. Necessary and sufficient conditions are established for the existence of solutions to the DSP. A complete parametrization of stabilizing controllers for the 2 × 2 case is given. Conditions of nonsolvability and hence nonstabilizability yield an explicit expression for the fixed modes of the system.