Robust Stability for Multiagent Systems with Spatio-Temporally Correlated Packet Loss

A problem with considering correlations in the analysis of multiagent system with stochastic packet loss is that they induce dependencies between agents that are otherwise decoupled, preventing the application of decomposition methods required for efficient evaluation. To circumvent that issue, this paper is proposing an approach based on analysing sets of networks with independent communication links, only considering the correlations in an implicit fashion. Combining ideas from the robust stabilization of Markov jump linear systems with recently proposed techniques for analysing packet loss in multiagent systems, we obtain a linear matrix inequality based stability condition which is independent of the number of agents. The main result is that the set of stabilized probability distributions has non-empty interior such that small correlations cannot lead to instability, even though only distributions of independent links were analysed. Moreover, two examples are provided to demonstrate the applicability of the results to practically relevant scenarios.