THE DISTURBANCE DECOUPLING PROBLEM FOR SYSTEMS OVER A RING

Up to now the use of geometric methods in the study of disturbance dec oupling problems (DDPs) for systems over a ring has provided only nece ssary conditions for the existence of solutions. In this paper we stud y such problems, considering separately the case in which only static feedback solutions are allowed, and the one in which dynamic feedback solutions are admitted. In the first case, we give a complete geometri c characterization of the solvability conditions of such problems for injective systems with coefficients in a commutative ring. practical p rocedures for testing the solvability conditions and for constructing solutions, if any exist, are given in the case of systems with coeffic ients in a principal ideal domain (PID). In the second case, we give a complete geometric characterization of the solvability conditions for systems with coefficients in a PID.