Simultaneous stabilization of single-input single-output discrete time systems

The problem of finding one compensator which simultaneously stabilizes a family of single-input-single-output (SISO) discrete-time plants is considered. The family of plants is described by the transfer functions {Pz, q): q∈Q}, which are generated via a z-transformation. A number of assumptions describing the set of allowable plants are then given. These assumptions include some regularity conditions on the plants and a minimum-phase requirement. The satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator C(z) for simultaneous stabilization. An iterative computation method is provided for control design