A constructive approach for distributed estimation under time-varying graphs

This work addresses the problem of distributed state estimation for jointly observable linear systems over periodic time-varying graph, which does not require the connectivity of the network for every time instant. We allow communication topology to be even disconnected for all t = 0, while only the weakest assumption of uniform connectivity on average is required. The problem is solved via a novel constructive method for averaging stability, which relies on a delay-free transformation along with a novel system presentation. This latter employs rapidly-varying scalar coefficients with zero averages rather than time-varying matrices, which leads to less conservative LMI-based stability criteria with improved upper-bound on the e-period preserving the exponential stability of the estimation error. Compared to the existing literature on the topic, we provide a quantitative approach for distributed state estimation over periodic communication graph, where the switching frequency is usually found only via simulation analysis. Numerical results show the effectiveness of the theoretical derivation.