Stability and consensus for multi-agent systems with Poisson clock noise

This paper is motivated by the problem of coordinating a group of autonomous agents with asynchronous, uncertain clocks. Timing uncertainty is commonly studied in networked control, but most work focuses on a single controller. Coordination problems also have a large literature, but the effect of uncertain, asynchronous timing is less understood. This paper studies multi-agent systems in which each agent has linear dynamics and a simple stochastic clock derived from a Poisson process. Necessary and sufficient conditions for stability are given based on linear matrix inequalities (LMIs). The analysis is then applied to networked control with random sampling times, as well as an asynchronous consensus protocol.