  The paper considers a distributed robust estimation problem over a network
with Markovian randomly varying topology. The objective is to deal with network
variations locally, by switching observer gains at affected nodes only. We
propose sufficient conditions which guarantee a suboptimal $H_\infty$ level of
relative disagreement of estimates in such observer networks. When the status
of the network is known globally, these sufficient conditions enable the
network gains to be computed by solving certain LMIs. When the nodes are to
rely on a locally available information about the network topology, additional
rank constraints are used to condition the gains, given this information. The
results are complemented by necessary conditions which relate properties of the
interconnection graph Laplacian to the mean-square detectability of the plant
through measurement and interconnection channels.
