  This paper deals with the H2 suboptimal state containment control problem for
homogeneous linear multi-agent systems and the H2 suboptimal output containment
control problem for heterogeneous linear multi-agent systems. For both
problems, given multiple autonomous leaders and a number of followers, we
introduce suitable performance outputs and an associated H2 cost functional,
respectively. The aim is to design a distributed protocol by dynamic output
feedback that achieves state/output containment control while the associated H2
cost is smaller than an a priori given upper bound. To this end, we first show
that the H2 suboptimal state/output containment control problem can be
equivalently transformed into H2 suboptimal control problems for a set of
independent systems. Based on this, design methods are then provided to compute
such distributed dynamic output feedback protocols. Simulation examples are
provided to illustrate the performance of our proposed protocols.
