Geometric characterization of reduced-order dynamic observer error linearization for uncontrolled multi-output systems

In this paper, we introduce the concept of reduced-order dynamic observer error linearization (RDOEL) for uncontrolled multi-output systems, which is a natural extension of the (conventional) observer error linearization (OEL) as well as a modified version of dynamic observer error linearization (DOEL). We first state necessary conditions for RDOEL, and then provide a necessary and sufficient condition in terms of Lie algebras of vector fields, which has not yet been completely established even in OEL.