On Observability Analysis for a Class of Uncertain Nonlinear Systems with Biased Observation

The paper studies the observability problem for a class of system with both uncertain nonlinear dynamics and measurement bias. Since none of the state vector, the uncertain dynamics and the bias can be modeled by an independent system, all their observability are comprehensively analyzed. Moreover, it is shown that the augmented state consisting of original state, uncertain dynamics as well as bias can not be observable. Thus, there always exists nonzero steady estimation error for any observer under uncertain dynamics and measurement bias in systems. The paper also discusses the observable augmented state combinations. After that an observer is constructed for an observable state that is close to the original state. Furthermore, the bound for the estimation error of original state is quantitatively discussed. Finally, some cases are presented so as to illustrate the theoretical results.