Event-triggered fixed-time multiple-leaders consensus under matrix-weighted communication

Abstract In this paper, we address the fixed-time multiple-leaders consensus problem for nonlinear multi-agent systems with uncertain disturbances. Matrix-weighted networks are employed to delineate interrelationships among multi-dimensional states of agents. Then, using event-triggered techniques, appropriate fixed-time controllers are designed to achieve fixed-time consensus from a single leader to multiple leaders cases in matrix-weighted networks. Meanwhile, the occurrence of Zeno behaviour is ruled out through proof by contradiction. Furthermore, utilizing the Lyapunov functional approach, we present adequate criteria for achieving fixed-time consensus under matrix-weighted networks through the application of linear matrix inequalities. In conclusion, the theoretical results are confirmed through the validation of two simulation examples. Matrix-weighted networks, fixed-time consensus, multiple leaders and nonlinear multi-agent systems.