Doubly Coprime Factorizations for General Proper Systems by Using Reduced-Order Observer-Based Controllers

By using reduced-order observer-based controllers, explicit state-space realizations of doubly coprime factorizations for general proper systems are derived. The known results for strictly proper systems can be obtained from our factorizations as particular forms. Also, the physical significance of the resulting controller parameterization is analyzed. Finally, the interesting connections between these factorizations in the present paper using an auxiliary stable matrix and those given before without introducing an auxiliary stable matrix are revealed, which show two versions of doubly coprime factorizations can be obtained each other by simple computations