THE BLOCK-DECOUPLING PROBLEM FOR SYSTEMS OVER A RING

The decoupling problem by static-state feedback for a system with coef ficients in a ring is investigated using a geometric approach. The not ion of a precontrollability submodule, which captures the geometric as pects of the notion of controllability subset of the state space in th e present context, is introduced and it is used for stating solvabilit y conditions for the decoupling problem for a system with coefficients in a Noetherian ring. This result extends and improves previous resul ts concerning systems with coefficients in a principal ideal domain an d it fan, in particular, be used for dealing with decoupling problem i nvolving delay-differential systems.