General Parameterization of Stabilizing Controllers with Coprime Factorizations

This paper is concerned with the factorization approach to control systems. The factorization approach we use here assumes that the plant admits coprime factorizations. On the ohter hand, the set of stable causal transfer functions is a general commutative ring. The objective of this paper is to present that even in the case where the set of stable causal transfer functions is a general commutative ring, we can employ the Youla-parameterization for the parametrization of stabilizing controllers.