studied in this paper. We assume that each observer has access to a local measurement which may
be insufficient to provide the observability of the system, but the ensemble of all measurements in
the network guarantees the observability. In this condition, the objective is to design a distributed
state estimation approach such that, while the observers can exchange their estimated state vectors
under a communication network, the estimated state vector of each observer converges to the
state vector of the system. We consider a scenario when the communication links may fail and
rebuild over time and the communication network does not stay connected constantly. Accordingly,
the main contribution of the paper is to propose a distributed approach (with guarantees on the
feasibility of the design) such that the state vector of the system is estimated by each observer if the
union/joint of communication links in bounded intervals of time makes the network communication
graph connected. Moreover, we also consider a scenario when the LTI system is subject to external
disturbances and measurement noise. In this case, we derive sufficient conditions on the proposed
approach such that if the communication topology stays connected during links failure, a desired H∞
performance to attenuate the effect of external disturbances and measurement noise on estimation
errors is guaranteed. Simulation results show the effectiveness of the proposed estimation approach.
