Induced Coprime Factorization for Continuous-Time Systems with Delay

In this work we consider the case of continuous-time systems with delay. It is well known that control of such type of plant models are hard, even more if they happen to be unstable plant models. The Youla Kucera parameterization of all stabilizing controllers has proved to be a useful tool to achieve the required controller solution. At the core of the Youla Kucera parameterization lies the coprime factorization of the plant model together with the Bezout identity. However, synthesizing the different terms in $RH_{\infty}$ satisfying the Bezout identity can become cumbersome in the presence of time delay. Here we offer an alternative approach stating the resulting Bezout identity terms for such a case, given the Bezout identity terms when the plant model is without time delay. This approach substantially simplifies the process of synthesizing a stabilizing controller solution for such challenging plant models.