Strongly Stabilizing Controller Synthesis for a Class of MIMO Plants

The strong stabilization problem (i.e., stabilization by a stable feedback controller) is studied for unstable MIMO plants with arbitrary number of finitely many poles but no more than two blocking zeros in the extended right half plane. Simple strongly stabilizing controllers, of order not exceeding that of the plant, are obtained for such plants satisfying the parity interlacing property. Connections with earlier design methods are illustrated: for this particular class of plants, it is shown that a sufficient condition appearing in earlier publications is equivalent to the parity interlacing property and hence it is also necessary for the existence of strongly stabilizing controllers. The results are illustrated with numerical examples.