New results on doubly coprime fractional representations of generalized dynamical systems

This note first points out that the main results by Wang and Balas regarding the doubly coprime fractional representations for generalized dynamical systems have severe limitation in their applications, that is, the doubly coprime factorization obtained by Wang and Balas cannot characterize the parameterization of all properly stabilizing controllers when a system is singular, therefore, truly generalized. To remedy those results, two new doubly coprime factorizations have been developed here that will parameterize all properly stabilizing controllers for single-input or single-output cases. In addition, the new results can characterize the parameterization of all corresponding causal properly stabilizing controllers. Finally, the extension to the multiple-input-multiple-output case is presented.