Design of coupling strengths for consensus with time-varying delays

This paper proposes a method to design the coupling strengths in a multi-agent system in order to achieve consensus in arbitrary directed networks in the presence of input time-varying delays. A model transformation is carried out to convert the consensus problem into a stability one. Then, based on an appropriate Lyapunov-Krasovskii functional, sufficient conditions for consensus in multi-agent systems are derived, where the coupling strengths are given as variables of Linear Matrix Inequalities (LMI). The designed coupling strengths may enable consensus and also meet a specified convergence rate. Numerical simulations are provided to demonstrate the effectiveness of the proposed results.