Discrete-time Global Leader-Following Consensus of a Group of General Linear Systems Using Bounded Controls: the State Feedback Case

This paper studies the problem of global leader-following consensus of a group of discrete-time general linear systems with bounded controls. We construct a bounded state feedback control law for each follower agent in the group by using a multi-hop relay protocol, in which the agent obtains the information of other agents through multi-hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of real eigenvalues on the unit circle and the number of pairs of complex eigenvalues on the unit circle of the sub-system corresponding to the input, and the feedback gains are constructed from the adjacency matrix associated with the communication network. We show that these control laws achieve global leader-following consensus when the communication topology is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower agent.