Robust semi-global leader-following practical consensus of a group of linear systems with imperfect actuators

This paper considers the problem of semi-global leader-following consensus of a multi-agent system whose agent dynamics are represented by linear systems. The input output characteristics of the follower agent actuators, such as those of saturation and dead-zone, are imperfect, not precisely known, and subject to the effect of disturbances. Two consensus control algorithms, of the low-and-high gain feedback type and the low gain based variable structure control type, are proposed for solving the consensus problem. It is shown that both of these control algorithms achieve semi-global leader-following practical consensus in the presence of the imperfectness of the actuators when the communication topology among the follower agents is represented by a strongly connected and detailed balanced directed graph and the leader agent is a neighbor of at least one follower agent. The theoretical results are illustrated by numerical simulation.