  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 neighbours 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.
