Stability analysis of decentralized overlapping estimation scheme with Markovian packet dropouts

We study the stability of an overlapping decentralized estimation scheme in the presence of packet dropouts. Several estimation agents receive local measurement of a discrete-time system over packet-dropping links, and each one constructs its estimate based on the measurements and on the communication with other agents which is also vulnerable to failure. The fusion of estimates at each agent is done based on a consensus strategy. We model packet dropouts in each link as a two-state Markov chain with known probabilities. Necessary and sufficient conditions for the mean-square stability of the estimator are provided in the form of linear matrix inequalities (LMIs) based on theory of Markovian jump linear systems. Also, we provide another set of sufficient conditions of the mean stability and error covariance boundedness for Markovian and arbitrary packet dropouts.