Distributed Observer Design for Linear Systems to Achieve Omniscience Asymptotically Under Jointly Connected Switching Networks

The distributed observer problem is motivated by the case where the output information of the system is decentralized in different subsystems. In this scene, all the subsystems form an observer network, and each of them has access to only a part of output information and the information exchanged via the given communication networks. Due to the limitation of communication conditions among subsystems, the communication network is often time varying and disconnected. However, the existing research about the aforementioned scene is still not enough to solve this problem. To this end, this article is concerned with the challenge of the distributed observer design for linear systems under time-variant disconnected communication networks. The design method is successfully established by fixing both completely decentralized output information and incompletely decentralized output information into account. Our work overcomes the limitation of the existing results that the distributed observer can only reconstruct the full states of the underlying systems by means of fast switching. In the case of completely decentralized output information, a group of sufficient conditions is put forward for the system matrix, and it is proved that the asymptotical omniscience of the distributed observer could be achieved as long as anyone of the developed conditions is satisfied. Furthermore, unlike similar problems in multiagent systems, the systems that can meet the proposed conditions are not only stable and marginally stable systems but also some unstable systems. As for the case where the output information is not completely decentralized, the results show with the observable decomposition and states reorganization technology that the distributed observer could achieve omniscience asymptotically without any constraints on the system matrix. The validity of the proposed design method is emphasized in two numerical simulations.