Distributed non-fragile containment control of nonlinear multi-agent systems with time-varying delays

Distributed containment control for multi-agent systems with time delay is investigated, where the communication topology is directed. Different from the existing literature which mainly focuses on general linear dynamics with time delay, containment control of nonlinear dynamics is discussed with the help of a new follower-based time-varying delays control protocol. Furthermore, there always exist uncertainties in the controller and observer gain matrices, a novel class of non-fragile containment control with time delay is addressed for the first time, which can be more applicable and more significant to real physical systems. By making use of the convex analysis, algebraic graph theory, matrix transformation and Lyapunov theory, it is derived that the obtained results are cast as feasible linear matrix inequalities and the states of the followers finally converge to the convex hull formed by the leaders. Finally, two simulation examples of nine-agents topology are presented to verify the validity of obtained theoretical analysis.