H∞ consensus control of multi-agent systems with input delay and directed topology

In this study, the consensus problem for linear multi-agent systems with general directed graph in the presence of constant input delay and external disturbances is addressed. To deal with input delay, a truncated prediction of the agent state over the delay period is approximated by the finite-dimensional term of the classical state predictor. The truncated predictor feedback method is used for the consensus protocol design. By exploring certain features of the Laplacian matrix, the H∞ consensus analysis is put in the framework of Lyapunov analysis. The integral terms that remain in the transformed systems are carefully analysed using Krasovskii functional. Sufficient conditions are derived for the multi-agent systems to guarantee the H∞ consensus in the time domain. The feedback gain is then designed by solving these conditions with an iterative linear matrix inequality procedure. A simulation study is carried out to validate the proposed control design.