This paper discusses algebraic approaches of control design for a set of Single Input – Single Output (SISO) delayed systems that are further developed and discussed. The first principle utilises a special ring RQM, - a set of RQ-meromorphic functions. The second one is based on a ring of proper and stable rational functions RPS and can be considered as a special case. Controller parameters are derived through the general solution of linear Diophantine equations in the appropriate ring. A final controller can be tuned by the scalar real parameter m0>0. The methodology is illustrated by a comparison with another approach, some analyses of a tuning parameter and example. The simulations are performed in the Matlab environment.
