On Consensusability of Linear Interconnected Multi-Agent Systems and Simultaneous Stabilization

TL;DR

This paper investigates the conditions under which interconnected multi-agent systems can reach consensus, linking it to simultaneous stabilizability, and provides practical criteria validated through simulations of energy systems.

Contribution

It introduces a novel linear programming-based sufficient condition for consensusability in interconnected MASs and derives comprehensive necessary and sufficient conditions involving system parameters.

Findings

Weak physical couplings favor consensusability

Densely-connected graphs improve consensusability

Conditions validated through supercapacitor and microgrid simulations

Abstract

Consensusability of multi-agent systems (MASs) certifies the existence of a distributed controller capable of driving the states of each subsystem to a consensus value. We study the consensusability of linear interconnected MASs (LIMASs) where, as in several real-world applications, subsystems are physically coupled. We show that consensusability is related to the simultaneous stabilizability of multiple LTI systems, and present a novel sufficient condition in form of a linear program for verifying this property. We also derive several necessary and sufficient consensusability conditions for LIMASs in terms of parameters of the subsystem matrices and the eigenvalues of the physical and communication graph Laplacians. The results show that weak physical couplings among subsystems and densely-connected physical and communication graphs are favorable for consensusability. Finally, we validate our results through simulations of networks of supercapacitors and DC microgrids.