Leader-following Consensus Of Multi-agent Systems Over Fixed And Randomly Switching Topologies

This paper studies both continuous and discrete time leader-following consensus prob-lems for multi-agent systems with linear time-invariant agent dynamics over fixed and randomly switching topologies. In the system, the dynamics of each agent and the lead-er is a linear system. The switching is governed by a time-homogeneous Markov process, whose state corresponds to a possible interaction topology among agents. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented for both fixed and switching interaction topologies, which describe the information exchange between the multi-agent systems. It is shown that the effect of switching topologies on leader-following consensus is determined by the union of topologies associated with the positive recurrent states of the Markov process. Moreover, the effect of random link failures on discrete time leader-following consensus is investigated. The design technique is based on algebraic graph theory, Riccati inequality and Lyapunov inequality. Finally, the theoretical results are validated via simulations.