An iterative design procedure for simultaneous stabilization of MIMO systems

This paper considers the problem of finding one compensator which simultaneously stabilizes a family of MIMO plants. The family of plants {bdP(s, q): q ϵ Q}, represented by their transfer function matrices, may be uncountable thus allowing for the possibility of a continuum of variations in plant parameters. A “Hermite invariant factorization” of the plant is introduced and shown to be quite useful as far as stabilization is concerned. To obtain the desired results, a number of assumptions describing the set of allowable plants are imposed. These assumptions include some regularity conditions on the plant and MIMO versions of minimum phase and one sign high frequency gain requirements. The satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator C(s) guaranteeing simultaneous stabilization. The algorithm used for controller design has one most attractive feature, namely, it is recursive in nature and allows the designer to select one compensator coefficient at a time.