A Distributed Observer for a Continuous-Time Linear System with time-varying network

A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to design a gain $g$ in the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. A linear inequality for $g$ is provided when the network's graph is switching according to a switching signal with a dwell time or an average dwell time, respectively. It has also been shown the existence of $g$ when the stochastic matrix of the network's graph is chosen to be doubly stochastic under arbitrarily switching signals. This is accomplished by exploiting several well-known properties of invariant subspaces and properties of perturbed systems.