  We consider the global consensus problem for multi-agent systems with input
saturation over digraphs. Under a mild connectivity condition that the
underlying digraph has a directed spanning tree, we use Lyapunov methods to
show that the widely used distributed consensus protocol, which solves the
consensus problem for the case without input saturation constraints, also
solves the global consensus problem for the case with input saturation
constraints. In order to reduce the overall need of communication and system
updates, we then propose a distributed event-triggered control law. Global
consensus is still realized and Zeno behavior is excluded. Numerical
simulations are provided to illustrate the effectiveness of the theoretical
results.
