H∞ containment control for multi-agent systems over Markovian switching topologies

Improving the robustness performance of networking agents against external disturbance is quite necessary for the design of control protocols. This paper considers the robust containment control problem for a group of agents with linear dynamics over Markovian switching communication topologies. Considering the random switching of the communication graphs, this paper adopts the assumption that a continuous-time Markov process governs the switching of the communication topologies. To achieve containment, a class of distributed state-feedback controllers based solely on the relative information between neighboring agents is proposed. By using tools from graph theory and matrix theory, the containment control problem for a group of agents under the proposed controller is converted into the robust stability problem for a high-dimensional stochastic system. Sufficient conditions in the form of linear matrix inequalities are then given to ensure the existence of the state-feedback containment controller. It is worth mentioning that the proposed controller enables the networking agents to fulfill the containment control task when the external disturbance is absent, and to maintain good H_∞ robustness against disturbance when the external disturbance exists. A numerical simulation is finally performed on a group of helicopters to verify the theoretical results.