Semi-global state synchronization for discrete-time multi-agent systems subject to actuator saturation and unknown nonuniform input delay

This paper studies semi-global state synchronization of discrete-time homogeneous networks with diffusive full-state coupling or partial-state coupling subject to actuator saturation and unknown nonuniform input delay. We assume that agents are at most critical unstable, that is the agents have all its eigenvalues in the closed unit disc. The communication network is associated with an undirected and weighted graph, which is represented by a row stochastic matrix. In this paper, we derive an upper bound for the input delay tolerance, which explicitly depends only on the agent dynamics. Moreover, for any unknown delay less than the upper bound, we propose a linear static protocol for MAS with full-state coupling and a linear dynamic protocol for MAS with partial-state coupling based on a low-gain methodology such that state synchronization is achieved among agents for any initial conditions in a priori given compact set.