Decoupling of multivariable control systems over unique factorization domains

Necessary and sufficient conditions are established for the existence of a state variable feedback decoupling of an $m$-input, $m$-output time invariant linear control system over a unique factorization domain. An explicit computation is provided for the feedback and the feedforward gain matrix. Also necessary and sufficient conditions for the existence of a stability-preserving state feedback decoupling are given. The results are illustrated by some examples