Coprime Factorizability and Stabilizability of Plants by Adding Some Objects

This paper is concerned with the factorization approach to control systems. We consider the models in which some plants admit or do not admit coprime factorization. In the case where the plants admits only one-side coprime factorization, it is known that the plant with additional zeros admits both side coprime factorizations. However we show that in the case where the plant do not admit coprime factorization, there exists a case where the plant with any additional zeros cannot admit coprime factorization. We will also consider the parallel plants, in which one of them is plant to be stabilized. Any stabilizable plants has some parallel plants that admit both side coprime factorizations. However, we will show that unstabilizable plants is not able to construct such parallel plants.