On reaching weighted consensus for second-order delayed multi-agent systems

This paper investigated the weighted consensus problem of the second-order multi-agent systems. A novel second-order weighted protocol is designed and based on matrix theory and frequency domain method, some algebraic criteria are analytically proposed in cases of without and with time delays, respectively. According to the obtained results, it is found that the system can finally reach the specified state within a certain delay range by controlling the initial weights of the agents. Moreover, within the allowable delay range of the system, the final consensus state is independent of the system delay, but the system delay will affect the convergence rate of the system. Finally, the validity of our finding will be verified by several simulated experiments.