  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.
