Containment control of high-order multi-agent systems with heterogeneous uncertainties, dynamic leaders, and time delay

This paper deals with containment control of multi-agent systems where high-order canonical controllable linear systems with heterogeneous uncertainties are considered as the agents' dynamics. The leaders are dynamic with polynomial-type trajectories. In this paper, the control protocol is smooth and it is constructed from a flexible combination of local state feedback controller and a PI-type protocol. Utilizing this protocol, containment without suffering from chattering phenomena and consideration of any bound on the agents' states is achieved. In addition, the flexibility of this protocol helps the designer to reduce or even discard the inter-agent communication. Recalling the significant effects of time delay on the performance and stability of multi-agent systems, in this paper input time delay is also considered. Following a Lyapunov-Krasovskii stability approach, two linear matrix inequalities (LMIs) are derived, and then solving the LMIs' gains of the protocol are attained such that asymptotic stability of the multi-agent system under switching graph topology is guaranteed. Finally, the feasibility of the LMIs and the validity of the theoretical results are demonstrated through some numerical examples.