H2 suboptimal containment control of multi-agent systems

This paper deals with the distributed H
2
suboptimal containment control problem by static state feedback for linear multi-agent systems. Given multiple autonomous leaders, a number of followers, and an H
2
cost functional, we aim to design a distributed protocol that achieves containment control while the associated H
2
cost is smaller than an a priori given upper bound. To that end, we first show that the H
2
suboptimal containment control problem can be equivalently recast into the H
2
suboptimal control problem of a set of independent systems. Based on this, a design method is provided to compute such a distributed protocol. The computation of the feedback gain involves a single Riccati inequality whose dimension is equal to the dimension of the states of the agents. The performance of the proposed protocol is illustrated by a simulation example.