Discrete-time consensus strategy for a class of high-order linear multiagent systems under stochastic communication topologies

Achieving consensus in a class of high-order discrete-time multiagent systems is studied. It is supposed that the network topology is dynamic and the existence of a communication link between each two agents is stochastic. Based on the concept of discrete-time super-martingales, we propose a Lyapunov-based high-order protocol which guarantees achieving almost sure consensus in the network in the presence of some conditions. The main contribution of the paper compared with existing results for consensus control of high-order multiagent systems under stochastic networks is that the proposed consensus protocol in this paper requires no knowledge on the set of feasible topologies (topologies with nonzero probabilities), and can be designed without computing the eigenvalues of the coupling matrices associated with the feasible topologies. In this condition, the computational costs of the consensus protocol design will be decreased significantly. The results are validated via a numerical example.