Predefined containment control for general linear multiagent systems with time-varying delays and switching topologies

Containment control problems for general linear multiagent systems with switching interaction topologies and time-varying delays are studied. Firstly, state observers are constructed to estimate the multiple leaders under the influence of switching graphs and time-varying delays. Secondly, a predefined containment protocol is presented based on the distributed state observer, where the expected convex combination of multiple leaders is predefined by several given weights. Moreover, an algorithm with two steps to confirm the gain matrices of the containment protocol and state observer is given. Based on linear matrix inequality technique and common Lyapunov-Krasovskii stability theory, the convergence of this control strategy for multiagent systems with switching topologies and time-varying delays to achieve state containment is proved. Finally, a numerical simulation is given to verify the validity of the theoretical results.