Consensusability of First-Order Multiagent Systems Under Distributed PID Controller With Time Delay
Qian Ma, Shengyuan Xu · IEEE Transactions on Neural Networks and Learning Systems · 2021
This article analyzes the consensus of first-order multiagent systems under the network topology with a directed spanning tree. A distributed PID controller with time delay is designed. D-parameterization approach is used and the crossing set consisting of frequencies such that at least one characteristic root is on the imaginary axis is identified. It is proven that the rightward crossings of the characteristic roots are always guaranteed. The exact delay margin is then determined. Numerical simulation is proposed to demonstrate the theoretical analysis.