Distributed finite-time tracking control of high-order multi-agent systems with delay-dependent communications

In light of the stability theory for functional differential equations, the leader-following exponential consensus problem of multi-agent systems with communication delays is investigated. All the follower agents have identical MIMO linear dynamics which can be expressed in any order, and only the delayed state information of each agent is delivered through local communications. By combining the tools of algebraic graph theory, matrix theory and Riccati equation, it is analytically proved that the active leader will be followed by all the follower agents in finite time. Furthermore, a upper bound on the communication time-delay that can be tolerated for the high-order multi-agent systems is obtained. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the theoretical result.