Distributed H_∞ PID Feedback for Improving Consensus Performance of Arbitrary-delayed Multi-agent System

The H_∞ proportional-integral-differential (PID) feedback for arbitrary-order delayed multi-agent system is investigated to improve the system performance. The closed-loop multi-input multi-output (MIMO) control framework with the distributed PID controller is firstly described for the multi-agent system in a unified way. Then, by using the matrix theory, the prescribed H_∞ performance criterion of the multi-agent system is shown to be equivalent to several independent H_∞ performance constraints of the single-input single-output (SISO) subsystem with respect to the eigenvalues of the Laplacian matrix. Subsequently, for each subsystem, the set of the PID controllers satisfying the required H_∞ performance constraint is analytically characterized based on the extended Hermite-Biehler theorem. Finally, the three-dimensional set of the decentralized H_∞ PID control parameters is derived by finding the intersection of the H_∞ PID regions for all the decomposed subsystems. The simulation results reveal the effectiveness of the proposed method.