Distributed node-to-node consensus of multi-agent systems with time-varying pinning links

In this paper, the distributed node-to-node consensus problem is addressed for a class of linear multi-agent systems with time-varying pinning links by using relative state feedback. The coordination goal in the present work is to make the states of each follower track those of its corresponding leader asymptotically where only a small fraction of followers can sense the states of their corresponding leaders through some switched communication channels. By using tools from M-matrix theory and stability analysis of switched systems theory, it is theoretically shown that such a node-to-node consensus in the closed-loop multi-agent systems can be guaranteed if each follower can be directly or indirectly influenced by at least one leader over some uniformly bounded time intervals, with the inner coupling matrix as well as the coupling strength being appropriately designed. Distributed node-to-node consensus for multi-agent systems with general Lipschitz-type nonlinear dynamics is also investigated. Numerical simulations are finally performed to verify the effectiveness of the theoretical results.