Semi-Global Consensus Problems of Discrete-Time Multi-Agent Systems in the Presence of Input Constraints

This paper studies the consensus problems of the discrete-time multi-agent systems (MASs) in the presence of input saturation constraints over directed communication networks. Two kinds of consensus problems, of the leaderless consensus problem with no leader agent and the containment control problem with multiple leader agents, are investigated in this paper. Low gain feedback consensus algorithms based on the improved discretetime parametric algebraic Riccati equation (ARE) are proposed to solve the consensus problems. For the MAS without any leader, the trajectories of all agents converge together when the communication networks contain a directed spanning tree. For the MAS with multiple leaders, the trajectories of all follower agents converge to the convex hull spanned by the leader agents when there is at least one leader agent which is trackable for each follower agent. Simulation examples are provided to verify the theoretical results.