Leader-following consensus of switched multi-agent systems with communication time delay

The article investigates the leader-following consensus problem of switched multi-agent systems with communication time delay under arbitrary switching signals. Firstly, the multi-agent system is modeled as a switched linear system. Next, a consensus protocol is proposed, where the value of the control gain matrix can be obtained by using Riccati inequality or linear matrix inequality. Further, the conditions that make the system reach stability are given according to the Lyapunov–Krasovskii functional analysis and Common Lyapunov function respectively and the latter method provides an upper bound on the communication time delay to achieve consensus for the system. In the end, the validity of the above method is verified through an example.