Leader-following consensus of second-order multi-agent systems with arbitrarily appointed-time prescribed performance

In this brief, a novel leader-following appointed-time consensus control protocol is investigated for second-order multi-agent systems on a directed graph from the prescribed performance perspective. Through developing a new state-independent performance function, the practically fixed-time stability or expected appointed-time tracking accuracy of the leader-following network systems can be achieved, wherein, the state-independent setting time can be arbitrarily specified a priori. Compared with the existing works, the primary advantage of the proposed control protocol is that no fractional power state feedback is used and the transient behaviours including the appointed-time convergence rate, overshoot and undershoot can be synthesised simultaneously. Moreover, the excellent disturbance suppression capacity can be achieved just through adjusting a few parameters involved in the newly developed performance controller. Finally, two groups of illustrative examples are employed to validate the effectiveness of the proposed control protocol.