Second-order Consensus for Multi-Agent Systems With Time-Varying Delays Based on Delay-Partitioning

A consensus problem for second-order agents network with time-varying delays under the directed fixed topology is investigated in this paper. For the convenience of analysing, the original system is converted into an equivalent system associated with disagreement terms. By applying a variable delay-partitioning method, increased computational complexity is solved and obtain less conservatism. A suitable Lyapunov-Krasovskii functional (LKF) is constructed, combining the reciprocally convex combination lemmas with Wirtinger-based inequality to deal with integral items for the derivative of the LKF and further reduce the conservatism. Following the linear matrix inequality theory, a sufficient condition is presented to make all agents asymptotically reach consensus. Finally, simulations are given to illustrate the effectiveness of the proposed results.