Improved fixed-time consensus of delayed nonlinear leader–follower multi-agent systems

This article aims to study the problem of fixed-time consensus for nonlinear leader–follower multi-agent systems (MASs) with time delay. Firstly, a new fixed-time stability lemma is derived, where the condition of inequality contains a time-delayed term. Furthermore, a more precise estimated value of settling time (ST) including delayed parameter is obtained, which is different from those existing fixed-time stability lemmas. Thereby, it provides some options for designers in many practical scenarios when considering the delayed systems. Secondly, for the purpose of explaining its applicability, fixed-time consensus of leader–follower nonlinear MASs is investigated by designing a nonlinear control protocol including constant time delay. The designed protocol not only guarantees fixed-time consensus but also effectively improves the convergence rate. With the new proposed lemma, a novel consensus criterion is designed. This is the first time to obtain the time-delayed dependent fixed-time stability criterion for MASs. Finally, the validity and superiority of the established theoretical results are confirmed by one numerical simulation.