Time-Varying Trajectory Tracking Formation H∞ Control for Multiagent Systems With Communication Delays and External Disturbances

Time-varying formation (TVF) and trajectory tracking
$H_{\infty }$
control problem of multiagent systems (MASs) subject to communication delays and external disturbances under the directed communication topology is studied. This article’s objective is for all agents to attain the desired TVF and track the pregiven formation center trajectory simultaneously. First, a distributed TVF and trajectory tracking control protocol employing neighborhood interaction information is developed in the presence of communication delays. Second, since the Laplacian matrix of a graph can be decomposed into the product of two specific matrices, the TVF and trajectory tracking
$H_{\infty }$
control problem is converted into the lower dimension asymptotic stability problem of a closed-loop system by applying an appropriate variable conversion. Third, a Lyapunov–Krasovskii functional is constructed to analyze the stability of MASs. Sufficient conditions are obtained in the form of linear matrix inequalities (LMIs) to ensure the completion of the TVF and formation center trajectory tracking of MASs. In the meantime, the maximum allowable communication delay can be calculated by the LMIs. Finally, the results of numerical simulations are presented to verify the validity of the approach this article proposes.