H_∞ dynamic observers for a class of nonlinear systems with unknown inputs

Abstract

This paper presents a new approach to $H_{\mathrm{\infty }}$ observer design for a class of nonlinear systems with unknown inputs. The considered systems are composed of a linear part perturbed by an additive Lipschitz nonlinearity in the presence of unknown inputs and disturbances. Our objective is to present a dynamical observer which generalises the Luenberger observer, called also the Proportional Observer (PO), and the Proportional-Integral Observer (PIO). The advantages of this observer are its robustness with respect to uncertainties and modelling errors and its steady-state accuracy. The presented method also unifies the reduced and the full-order design. An example using a one-link-flexible joint robot is given to illustrate our approach.

Keywords:

• Dynamic observer
• nonlinear systems
• Lipschitz nonlinearities
• LMIs

Disclosure statement

No potential conflict of interest was reported by the authors.