Consensus problems for linear time-invariant multi-agent systems with saturation constraints

A class of networked multi-agent systems is studied in this study where each agent has an identical dynamics of a simple integrator and the topology of the connections is fixed. It is proved that, when there are saturation constraints, a general consensus protocol widely used in the literatures for this class of multi-agent systems remains valid. As an extension, a `bang-bang` type of consensus protocol is proposed to achieve the finite-time consensus, which relaxes the previous undirected connection assumption.