Stabilization of Nonlinear Systems and Coprime Factorization

In this paper, the problem of constructing a right coprime factorization of a system is considered. The approach is based on the concept of right-coprimeness introduced recently and on a stabilizing state feedback. Since our approach does not require construction of solutions to a Bezout identity, the construction of a stabilizing output injection is not needed. Some relationships between the existence of stabilizing output feedbacks and solutions to Bezout identities for (time-varying) linear systems are discussed and a development of left-coprime factorization of a nonlinear system is presented. We also prove that the existence of two coprime factorizations will imply the existence of the other two when the plant and the controller are both linear and the unity feedback system is finite-gain stable.