Optimal rejection of bounded perturbations in linear leader-following consensus protocol: invariant ellipsoid method

The objective of the invariant ellipsoid method is to minimize the smallest invariant and attractive set of a linear control system operating under the influence of bounded external disturbances. This study extends the application of this method to address the leader-following consensus problem. Initially, a linear control protocol is designed for the multi-agent system in the absence of disturbances. Subsequently, in the presence of bounded disturbances, by employing a similar linear control protocol, a necessary and sufficient condition is introduced to derive the optimal control parameters for the multi-agent system such that the state of followers converges to and remains in a minimal invariant ellipsoid around the state of the leader.