Fixed-time event-triggered consensus of second-order multi-agent systems with fully continuous communication free

This study deals with fixed-time consensus problems of second-order multi-agent systems with uncertain bounded disturbances. Instead of the time-triggered control algorithm, a distributed event-triggered control algorithm is developed in the presence of uncertain disturbance. By designing a novel threshold, a triggering function is proposed, which is fully distributed and does not require continuous communication. To tackle the chattering problem, a saturation function is defined to improve the control algorithm. Several conditions are derived and the rigorous proof is given by using Lyapunov stability theory and fixed-time stability theory. Then, to reduce the disturbance effect, an event-triggered control algorithm is proposed by using a disturbance observer. Finally, two simulation examples are given to verify the efficiency of the proposed control method.