  In view of the problems of large consumption of communication and computing
resources in the control process, this note studies a fundamental property for
a class of multi-agent systems under event-triggered strategy: the
S-stabilizability of a group of multi-agent systems with general linear
dynamics under weakly connected directed topology. The results indicate that
the S-stabilizability can be described in some way that the stabilizability
region and feedback gain can evaluate the performance of the protocol. Firstly,
a new distributed event-triggered protocol is proposed. Under this protocol, a
kind of hybrid static and dynamic event-triggered strategy are presented,
respectively. In particular, by using Lyapunov stability theory and graph
partition tool, it is proved that the proposed event-triggered control strategy
can guarantee the closed-loop system achieve S-stabilizability effectively, if
at least one vertex in each iSCC cell receives information from the leader,
which reflects the ability of distributed control law. Further, we demonstrate
that the stabilizability can be realized if the initial system matrix A is
Hurwitz. Moreover, it is confirmed that the designed static event-triggered
condition is a limit case of dynamic event condition and can guarantee
Zeno-free behavior. Finally, the validity of the theoretical results is proved
by numerical simulation.
