Distributed State Estimation of Linear Systems With Randomly Switching Communication Graphs

This letter introduces two novel methods to synthesize distributed observers for time-varying communication graphs which are modeled as continuous-time Markov processes. The first method obtains all design parameters in a centralized step by solving a system of coupled LMI, while the second method utilizes an observability decomposition to design the parameters locally by partitioning into observable and unobservable system parts. For both methods, this letter provides sufficient conditions for the existence of distributed observers which asymptotically achieve omniscience almost surely. A numerical example to compare the two methods is provided in addition.