This paper deals with a distributed state estimation problem for jointly observable multi-agent systems operated over various time-varying network topologies. The results apply when the system matrix of the system to be observed contains eigenvalues with positive real parts. They also can apply to situations where the communication networks are disconnected at every instant. We present sufficient conditions for the existence of distributed observers for general linear systems over periodic communication networks. Using an averaging approach, it is shown that the proposed distributed observer can provide exponentially converging state estimates of the state of the linear system when the network is uniformly connected on average. This average connectedness condition offers a more relaxed assumption that includes periodic switching, Markovian switching and Cox process switching as special cases. All the agents in the network share the estimated state with their neighbors through the network and cooperatively reconstruct the entire state locally. Furthermore, this study presents two exponential stability results for two classes of switched systems, providing valuable tools in related distributed state estimation approaches. A toy example and three practical applications are provided to illustrate the effectiveness of the theoretical results.

中文翻译：

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时变网络上联合可观测线性系统的分布式状态估计

本文研究了在各种时变网络拓扑上运行的联合可观测多智能体系统的分布式状态估计问题。当待观察系统的系统矩阵包含具有正实部的特征值时，结果适用。它们还可以应用于通信网络随时断开的情况。我们提出了周期性通信网络上一般线性系统的分布式观测器存在的充分条件。使用平均方法表明，当网络平均均匀连接时，所提出的分布式观测器可以提供线性系统状态的指数收敛状态估计。这种平均连通性条件提供了更宽松的假设，包括周期性切换、马尔可夫切换和 Cox 过程切换作为特殊情况。网络中的所有代理通过网络与邻居共享估计状态，并在本地协作重建整个状态。此外，本研究提出了两类切换系统的两个指数稳定性结果，为相关分布式状态估计方法提供了有价值的工具。提供了一个玩具示例和三个实际应用来说明理论结果的有效性。