Semi-global Output Feedback Stabilization of Non-Minimum Phase Nonlinear Systems

TL;DR

This paper presents a semi-global output feedback stabilization method for nonlinear systems with potentially unstable zero dynamics, utilizing an extended high-gain observer and Kalman filter for state estimation.

Contribution

It introduces a novel stabilization approach combining high-gain observers and Kalman filters for a broad class of nonlinear systems with unstable zero dynamics.

Findings

Semi-global stability of the closed-loop system achieved

Effective state estimation using combined high-gain observer and Kalman filter

Simulation confirms the practical applicability of the proposed method

Abstract

We solve the problem of output feedback stabilization of a class of nonlinear systems, which may have unstable zero dynamics. We allow for any globally stabilizing full state feedback control scheme to be used as long as it satisfies a particular ISS condition. We show semi-global stability of the origin of the closed-loop system and also the recovery of the performance of an auxiliary system using a full-order observer. This observer is based on the use of an extended high-gain observer to provide estimates of the output and its derivatives plus a signal used by an extended Kalman filter to provide estimates of the remaining states. Finally, we provide a simulation example that illustrates the design procedure.