The leaderless consensus problem for a class of Lipschitz nonlinear multi-agent systems is investigated under time-varying directed topologies. Communication uncertainties are introduced to model the possible transmission errors or information constraints. Both the cases of with and without communication uncertainties are considered. To overcome the effects of directed topology asymmetry, some novel results of the properties related to the graph Laplacian matrix are introduced. Based on this, consensus problem with directed switching topologies is converted to a stabilization problem of a lower dimensional switched consensus error system. Then, using common Lyapunov function based method and algebraic graph theory, sufficient conditions for reaching consensus under directed switching topologies with arbitrarily switching speed is derived. Finally, two simulation examples of flexible-joint manipulators are introduced to verify the effectiveness of the results.
Liu et al. (2026) studied this question.