Fixed-time distributed event-triggered formation control with state-dependent threshold

Since the complexity nonlinearities generated by discontinuous control and event-triggered scheme, fixed-time formation in event-based framework is a more challenging issue compared with the continuous-time control. This paper focuses on fixed-time leaderless formation problem for multi-agent systems with undirected topology. We propose a distributed robust event-triggered control strategy for the fixed-time formation where predictor-based state transformation is employed to deal with input delay and sliding mode technology is implemented to solve bounded disturbances. We also obtain that the upper bound of the formation settling time is only determined by delay time, control design parameters, network connectivity, and independent of the initial conditions. In addition, the lower bound for the interexecution time is calculated to ensure that there is no Zeno behavior occurs. Finally, some numerical simulations are presented to show the effectiveness of the strategies.