A Linear Filtering Framework for Nonlinear Systems Based on Extended Output Injection

Abstract

The problem of transforming a single-output, nonlinear state equations affine in disturbances into an extended observer form using a state diffeomorphism is addressed. The dynamics of this form consists of a linear component in the dual-Brunovsky observer canonical form, and a nonlinear output-injection term which is affine in the disturbance, and depends only on the output and its first $l$ derivatives. The intrinsic geometric necessary and sufficient conditions (directly verifiable from the state space form) for the existence of such state transformation, are obtained. The extended observer form is used in designing a Kalman-filter based observer with exponentially attractive error dynamics, which is stable in the input-to-state (ISS) sense with respect to the disturbance, assuming that the output and its first $l$ derivatives are directly measurable or can be accurately estimated.