Prescribed-time Lag consensus, as a special case of prescribed-time cluster lag consensus, is first investigated. The task is to design a control protocol for each follower so that the multiagent system (MAS) achieves lag consensus in any specified time. To achieve this goal, we propose a new distributed controller, in which the control gains are designed as time-varying functions related to the pre-specified time. In addition, a state transformation is introduced to tackle the technical difficulty caused by time-varying functions of different powers in the theoretical proof process. Then, a solution for the cluster lag consensus problem of the MAS is provided, so that under the proposed control protocol, each subsystem composed of followers from the same group and the leader achieves lag consensus with a different lag time in the specified time. By using a state transformation, Graph theory and generalized Lyapunov stability theory, the validity of the designed schemes is verified theoretically and sufficient conditions for the two conclusions are given respectively. Finally, we give two simulation examples to show performances of the proposed solutions.

首先研究了规定时间滞后共识，这是规定时间簇滞后共识的特例。任务是为每个跟随者设计一个控制协议，以使多代理系统（MAS）在任何指定时间内均达到滞后共识。为了实现这一目标，我们提出了一种新的分布式控制器，其中将控制增益设计为与预定时间相关的时变函数。另外，引入了状态变换来解决在理论证明过程中不同权力的时变函数所引起的技术难题。然后，针对MAS的集群滞后一致性问题提供了一种解决方案，从而在所提出的控制协议下，由同一组的跟随者和领导者组成的每个子系统在指定时间内以不同的滞后时间达成滞后共识。通过状态变换，图论和广义Lyapunov稳定性理论，从理论上验证了所设计方案的有效性，并分别为两个结论给出了充分的条件。最后，我们给出两个仿真示例来说明所提出解决方案的性能。