Responsible Eigenvalue Approach for Stability Analysis and Control Design of a Single-Delay Large-Scale System With Random Coupling Strengths

A class of linear time-invariant (LTI) consensus system with multiple agents and communication delays among the agents is studied. The delay margin of this MIMO system, that is, the largest amount of the delay that the system can withstand without loosing stability, can be studied by the authors’ Responsible Eigenvalue (RE) concept. RE is able to compress the considered stability problem into the stability problem of a single agent system, from which RE captures the delay margin of the entire MIMO system. RE is used here to design controllers for the MIMO system for the objective of increasing the delay margin. Case studies demonstrate connections between coupling strengths, graph Laplacian, the delay margin of a large-scale consensus system, and control synthesis.