Design of Distributed Observers in the Presence of Arbitrarily Large Communication Delays

This paper focuses on the construction of distributed observers in the presence of arbitrarily large communication time delays. In contrast with the traditional centralized observer with the ability to acquire full output of the plant, we design a set of distributed observers, each having access to partial output of the plant through a distributed sensor network. More specifically, each observer obtains partial plant output and communicates with its neighboring observers through consensus protocols. The communication among the network is subject to arbitrarily large time delays. We consider three representative network topologies and for each topology establish conditions to guarantee the observation error systems be exponentially stable. We also consider the design of a pinning synchronization problem as a dual problem of the design of distributed observers. Numerical simulation is carried out to verify the effectiveness of our theoretical analysis.