Reduced-order dynamic observer error linearisation: a natural extension of observer error linearisation

This paper introduces the concept of reduced-order dynamic observer error linearisation (RDOEL) for multi-output systems, which is the problem of transforming a nonlinear system into a nonlinear observer canonical form with the aid of auxiliary dynamics. The proposed RDOEL framework is not only a modified version of dynamic observer error linearisation (DOEL) but also a natural extension of observer error linearisation (OEL). We provide three necessary conditions for the RDOEL problem, and then derive a necessary and sufficient condition described in terms of Lie algebras of vector fields. Furthermore, from the result, we also give a geometric necessary and sufficient condition for the OEL problem, which has not yet been completely established in the case where a diffeomorphism on the output of general form is considered.