Second-order consensus of multi-agent systems with mixed delays and uncertain parameters via adaptive pinning aperiodically intermittent control

This paper investigates the second-order consensus of multi-agent systems with mixed delays and uncertain parameters. On one hand, an adaptive pinning aperiodically intermittent control protocol is designed to make multi-agent systems reach the second-order consensus. Moreover, the intermittent control protocol can be designed to be aperiodic, which means each agent can only obtain the relative states’ information from its neighbours at a sequence of disconnected aperiodic time intervals. On the other hand, based on the assumption that delay is less than the width of communication time, some consensus criterions in the form of matrix inequalities are derived by using Halanay inequality, Jensen inequality and Schur complement. At last, a simulation example is given to illustrate the correctness of the theoretical analysis.