The decoupling problem with weak output controllability for systems over a ring

The paper is devoted to the study of the decoupling problem for systems with coefficients in a ring. The problem is stated in a so-called weak form, which does not require the complete output controllability. Necessary and sufficient conditions are found for the existence of solutions in the form of dynamic state feedbacks, for systems with coefficients in a Noetherian ring. Applications to the block decoupling problem for time-delay systems are described.