H∞ Consensus for Heterogeneous Multi-agent Systems with Time-delay

In this paper, we consider the consensus and H_∞ consensus problems of heterogeneous multi-agent systems composed of first-order and second-order integrator agents in directed networks with time-delay. Based on the graph theory and the reduced-order transformation, we first rewrite the heterogeneous multi-agent systems into the corresponding reduced-order systems. Then, we study the consensus of the heterogeneous multi-agent system with time-delay by using the linear matrix inequality method. As a result, sufficient conditions for consensus and H_∞ consensus of heterogeneous multi-agent systems in terms of linear matrix inequalities are established. Finally, simulation results are provided to demonstrate the effectiveness of the main theoretical results.