On performance analysis of extended state observer for a class of systems with multiple uncertainties and biased measurement

This paper studies the state estimation problem of a class of systems with multiple uncertainties and biased measurement. Since the observability of such system is not satisfied, the estimations for states and uncertainties definitely have biases. For the extended state observer which aims to estimate the system states and the dominant term of uncertainties, the quantitative estimating performance is studied in the paper. Furthermore, the biased estimation error is explicitly shown, which can be derived from the following three parts: 1) the biased measurement; 2) the unobservable dominant uncertainty; 3) the non-dominant term of multiple uncertainties. The theoretical analysis in the paper can help practitioners quantitatively evaluate the effectiveness of the designed extended state observer.