H2 consensus control of time-delayed multi-agent systems: A frequency-domain method

•Multi-input multi-output block diagram in frequency domain is introduced to describe the consensus tracking of multi-agent systems.•Consensus tracking condition imposed on the controller is given.•Analytical controller is designed for the consensus of homogeneous multi-agent systems with input time delays to improve the H2 performance index.•Simple quantitatively tuning way is developed to trade off the nominal performance and robustness.

An analytical H2 controller design approach of homogeneous multi-agent systems with time delays is presented to improve consensus performance. Firstly, a closed-loop multi-input multi-output framework in frequency domain is introduced, and a consensus tracking condition is given. Secondly, the decomposition method is utilized to simplify the analysis of internal stability and H2 performance index of the whole system to a set of independent optimization problems. Finally, the H2 optimal controller can be computed from all the stabilizing controllers. The contributions of the new approach are that the design procedure is conducted analytically for arbitrary delayed multi-agent systems, and a simple quantitative tuning way is developed to trade off the nominal performance and robustness. The simulation examples show the effectiveness of the proposed control strategy.