Reduced-order Dynamic Observer Error Linearization (proofs included)

Abstract

For an unforced nonlinear single output system, we propose a modified version of dynamic observer error linearization (DOEL) that is called reduced-order dynamic observer error linearization (RDOEL). The approach offers a lower dimensional observer than DOEL, and allows a complete constructive algorithm in contrast to DOEL when the auxiliary dynamics is a chain of integrators. In this paper, we describe the initial stage of the algorithm for RDOEL with integrators (RDOELI), and derive a complete solution to a simple case of DOEL through the discussion of the relation among RDOELI, DOEL, and system immersion.