Distributed Interval Observer and Distributed Unknown Input Observer Designs

Recently, distributed observer designs have been investigated intensively, but the distributed unknown input observer (DUIO) which can offer the asymptotic convergent estimations of both the states and the unknown inputs (UIs) has not been developed yet. In this paper, we come up with a novel DUIO design method through a distributed interval observer (DIO) for a system with UI, and each sensor with measurement noise. First, by introducing an auxiliary output, the local system is transformed into a system where the output contains no measurement noise. Then, a DIO is designed. Based on the DIO, a relationship between the UI and the state is established algebraically. By taking advantage of the algebraic relationship, a DUIO which is composed of a general distributed observer and an unknown input reconstruction (UIR) is constructed. The DUIO offers the asymptotic convergent state estimation and UIR. After this, asymptotic convergent measurement noise reconstruction is also provided. Finally, a simulation example is given to verify the effectiveness of the proposed method.