Generalised dynamic observer design for Lipschitz non-linear descriptor systems

Abstract

This study concerns the observer design for Lipschitz non-linear descriptor systems. It introduces a new observer structure called a generalised dynamic observer, which is more general than the proportional and proportional-integral observers. The originality of the proposed observer is that it provides additional degrees of freedom in the observer design, which can be used to increase steady-state accuracy and to improve robustness in estimation against modelling errors. Conditions for the existence and stability of this observer are given in terms of linear matrix inequalities. Reduced-order and fullorder observers can be designed directly by using the proposed unified approach. The effectiveness of the developed method is illustrated by two numerical examples where impulse and impulse-free cases are considered, a comparison between the generalised dynamic observer, the proportional observer, and the proportional-integral observer is given to show the observers performances.