Consensus tracking of general linear multi-agent systems: Fast sliding-mode algorithms

This paper solves distributed consensus tracking problems where the task is to make the multi-agent network, with each agent described by a general linear dynamics, to reach consensus with a leader whose control input is nonzero and not available to any followers. A set of sliding mode surfaces are defined and then fast sliding mode controllers are designed for both reduced order and non-reduced order cases. It is shown that all the trajectories exponentially converge to the sliding mode surfaces in a finite time if the leader has a directed path to at least one of the followers in a strongly connected and detailed balanced directed interaction graph and the leader´s control input is bounded. The control Lyapunov function for exponential finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surfaces. Simulation examples are given to illustrate the theoretical results.