Using coprime factorizations in partial decoupling of linear multivariable systems

Examines the problem of partial (upper or lower triangular) decoupling in a one-degree-of-freedom feedback configuration. The approach taken is based on the use of coprime factorizations over the ring of proper and stable rational functions, which provides a direct understanding of issues such as internal stability. Within this framework, both necessary and sufficient conditions for partial decoupling are studied and, as a consequence, a design method for partial decoupling control is presented. A parametrization of the set of all partial decoupling controllers is also given. Finally, diagonal decoupling is considered as a particular case of partial decoupling, indicating how the corresponding links with related work on diagonal decoupling and coprime factorizations can be obtained