Dynamic observer error linearization

In this paper, a new framework of observer error linearization problem is proposed. The main idea of our approach is twofold. The one is to introduce an auxiliary dynamics whose input is the system output, and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics. It is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output. It is also shown that whenever an n dimensional system is immersible into an n+d dimensional linear system up to an output injection, then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics. Moreover, we show that the converse is not true by providing a counterexample, which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method.