Block triangular decoupling for linear systems over principal ideal domains

This paper studies in the framework of the so-called geometric approach the block triangular decoupling problem with state feedback for linear systems defined over a principal ideal domain with identity. First, various properties of feedback reachability submodules are discussed, and then under certain assumptions necessary and sufficient conditions for its solvability are obtained. Further, the pole assignability for decoupled systems is investigated. Finally, a simple example is given to illustrate the results.