Leader-following consensus of the second-order multi-agent systems under directed topology

This paper investigates the consensus problem for second-order multi-agent systems with a dynamical leader. A simple and novel protocol based on the relative state of the neighboring agents is proposed. Using the linear matrix inequality method, sufficient conditions are derived to ensure the consensus for both the cases without and with communication delay in the multi-agent systems. Some numerical simulations are also given to show the effectiveness of the proposed results. •We investigate the leader-following consensus problem for the second-order multi-agent systems under directed topology in this paper.•Two novel protocols are designed for reaching the consensus for both the cases without and with communication delay in the multi-agent systems.•Some discussions on consensus tracking with switching directed topology are given in this paper.•Some numerical examples are given to demonstrate the effectiveness of the proposed criteria.