SIMULTANEOUS STABILIZATION OF SINGLE-INPUT SINGLE OUTPUT DISCRETE-TIME-SYSTEMS

This note considers the problem of finding one compensator which simul taneously stabilizes a family of single-input single-output (SISO) dis crete-time plants. The family of plants is described by the transfer f unctions {P(z, q):q is-an-element-of Q} which are generated via the z- transformation adopted in [1] and [2]. A number of assumptions describ ing the set of allowable plants are then given. These assumptions incl ude some regularity conditions on the plants and a minimum-phase requi rement. The satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator C(z) for simultaneous stabili zation. An iterative computation method is provided for control design .