Distributed Observer Design of Linear Systems with Time-Varying Topologies

This paper proposes a distributed observer for linear time-invariant (LTI) non-autonomous systems. The observer can handle time-varying topologies. Based on multi-hop communication and Volterra operator, all nodes can reconstruct the global state within a fixed time. The concept of 'freshness' is introduced to update the information used for estimation in real-time, so that the observer can instantaneously respond to topology changes. When the changes prevent nodes from obtaining sufficient information from their neighbors, the algorithm automatically switches to open-loop prediction to ensure reconstruction. Compared with existing methods, the algorithm proposed in this paper relaxes the common joint strong-connectivity assumption and is applicable to more general non-autonomous systems, significantly improving its practicality. Finally, the effectiveness and robustness of the proposed observer were verified through numerical simulations in both noise-free and noisy scenarios.