Generalized containment control for delayed fractional-order nonlinear multi-agent systems with unknown disturbances

In this article, the issue of generalized containment control is explored for a class of delayed fractional-order nonlinear multi-agent systems (MASs) with unknown disturbances. It is assumed that the MAS under consideration has multiple dynamic leaders, and its dynamics are governed by fractional-order differential equations, and suffers from the unknown but norm-bounded external disturbances. Also, the directed graph of the MAS is assumed to have a united directed spanning tree. Furthermore, for the sake of saving communication resources, an event-triggered mechanism is introduced to regulate the signal transmission. In the presence of the external disturbances, the generalized containment control is analyzed by means of Lyapunov stability theory, algebraic graph theory, Halanay-type inequality, etc., and sufficient conditions are established to ensure that all followers ultimately enter a certain neighborhood of the convex hull formed by the leaders. In the meanwhile, it is also proven that the Zeno phenomenon can be excluded for the concerned MAS. Finally, a numerical simulation is presented to further illustrate the effectiveness of the theoretical results.