Fully distributed event-triggered consensus for nonlinear time-delayed multi-agent systems

In this paper, the fully distributed dynamic and static event-triggered consensus problem for nonlinear time-delayed multi-agent systems is investigated. In order to reduce the communication load, distributed consensus control protocols based on static and dynamic adaptive event-triggered mechanisms are designed, respectively. Using knowledge of graph theory, matrix theory, and Lyapunov stability theory, the sufficient conditions for the system to achieve consensus are rigorously derived, and the Zeno behaviour is excluded. By designing appropriate event-triggered conditions, thus reducing the frequency of update information among agents. In particular, the internal dynamic variables in the dynamic event-triggered mechanism can adjust their thresholds in real time, which is more flexible in the change process and further reduces the number of communications. Finally, the effectiveness and superiority of the two control strategies and the two event-triggered strategies are verified by a dual mass spring system example.