Decentralized PID controller design for the cooperative control of networked multi-agent systems

For the networked multi-agent system with arbitrary-order time-delayed agent dynamics, the parametric H
_∞
design method of the decentralized PID controller is proposed in this paper. The closed-loop framework representation is first given for the multi-agent system with the decentralized PID controller imposed on each agent. Based on this close-loop framework, the H
_∞
performance criterion of the entire system is transformed into several local H
_∞
performance constraints of the subsystem which is related to the eigenvalues of the Laplacian matrix. Thus, the design problem of the decentralized H
_∞
PID controller is converted to the stabilization problem of the PID controller simultaneously for a family of complex quasipolynomials. Then, two parametric approaches are given to determine the region of the PID control parameters that can guarantee the stability of the complex quasipolynomial. Finally, the decentralized H
_∞
PID controller is derived by finding the intersection of the stabilizing PID regions for all resultant quasipolynomials.