Group consensus for multi-agent systems with Lurie dynamics and time delays

The group consensus problem of nonlinear multi-agent systems with delayed Lurie-type dynamics is investigated in this paper. A pinning control scheme is designed under undirected communication graph. Firstly, a sufficient condition in terms of linear matrix inequalities(LMIs) is obtained to guarantee the group consensus in the multi-agent systems without disturbance. Then, a sufficient condition guarantee the group consensus in the multi-agent systems with external disturbances and desired performance is derived. Moreover, the notion of the consensus region is introduced. Numerical example is finally provided to verify and illustrate the theoretical results.