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.

中文翻译：

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联合连接交换网络下线性系统的分布式观测器设计以渐进地实现全知。

分布式观察者问题的动机是系统的输出信息分散在不同的子系统中。在这个场景中，所有子系统组成一个观察者网络，每个子系统只能访问一部分输出信息和通过给定通信网络交换的信息。由于子系统之间通信条件的限制，通信网络往往是时变和不连通的。然而，现有的关于上述场景的研究还不足以解决这个问题。为此，本文关注时变断开通信网络下线性系统分布式观测器设计的挑战。通过同时考虑完全分散的输出信息和不完全分散的输出信息，成功建立了设计方法。我们的工作克服了现有结果的局限性，即分布式观察者只能通过快速切换来重建底层系统的完整状态。在输出信息完全分散的情况下，为系统矩阵提出了一组充分条件，证明了只要满足任一展开条件，就可以实现分布式观察者的渐近全知。此外，与多智能体系统中的类似问题不同，能够满足所提出条件的系统不仅是稳定的和边际稳定的系统，而且还有一些不稳定的系统。对于输出信息不完全分散的情况，结果表明，利用可观测分解和状态重组技术，分布式观测器可以在不受系统矩阵任何约束的情况下渐进地实现全知。所提出的设计方法的有效性在两个数值模拟中得到强调。