Global Leader Following Consensus of a Group of Discrete-Time Linear Systems Using Bounded Controls

Abstract

This paper studies the global leader-following consensus problem for a group of discrete-time linear systems with bounded controls. For each follower agent, we construct a bounded nonlinear feedback control law which uses the information of other agents obtained through multi-hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents is no bigger than the largest algebraic multiplicity of the eigenvalues on the unit circle of the system matrix. 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.