Matrix measure-based distributed impulsive consensus on nonlinear multi-agent systems with mixed time-varying delays.

This paper concentrates on researching the global and exponential leader-following consensus issue for an array of nonlinear multi-agent systems with the system time-varying delay and the distributed time-varying delay. An innovative distributed impulsive controller is proposed to force the states of all agents to track the trajectories of leader agent. By jointly introducing the matrix measure protocol, the comparison principle for impulsive systems, and the average impulsive interval, sufficient criteria for the realization of leader-following consensus are derived. In addition, considering different functions of impulsive signal, two different convergence rates are precisely estimated by utilizing the parameter variation formula, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of proposed control strategy and the rightness of theoretical analysis. • Both the system delay and the distributed delay is considered in MASs; • An innovative distributed impulsive controller is designed, which increases the control flexibility and accelerates the speed of consensus; • The leader-following consensus is realized based on two different functions of impulsive effects. [ABSTRACT FROM AUTHOR]