Consensus of a class of multi-agent systems based on directed graph: Fixed and switching topology

This paper investigates the consensus problem for a class of linear multi-agent systems based on directed graphs (not necessarily balanced graphs), and provides a kind of more general control protocols for the fixed and switching topologies, respectively. First, by decomposition of the state space, a necessary and sufficient condition is obtained for the consensusability of the multi-agent systems with a fixed information topology under the general control protocol. Second, utilizing the obtained necessary and sufficient condition, a new algorithm is provided to find the final consensus state based on the given initial condition. Third, for the case of switching topology, a sufficient condition is proposed for the consensusability of multi-agent systems under the general control protocol, and it is shown that the state consensus can reach under the given conditions. Finally, several examples are studied with our presented method. Illustrative examples with simulations show that our method as well as control protocols work very well for the consensus problem of this class of linear multi-agent systems.