Consensus Problem in General Linear Multiagent Systems Under Stochastic Topologies

Consensus control of a class of multiagent systems with general linear dynamics is studied. Based on solution of some linear matrix inequalities, a protocol is obtained which guarantees achieving consensus among agents in the presences of stochastically switching topologies. By invoking the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, the agents reach almost sure consensus upon their state vectors. Despite existing results in the literature for consensus control of general linear multiagent systems under stochastic networks, the proposed consensus protocol in this paper requires no knowledge on the set of feasible topologies, and this issue significantly decreases the design computational costs. Simulation results for a diving consensus problem among a team of autonomous underwater vehicles validate the proposed consensus protocol.