Stability Analysis of Pinning Consensus Control of Discrete-time Multi-agent Systems

Dongwu XU  Akinori SAKAGUCHI  Toshimitsu USHIO  

A - Abstracts of IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (Japanese Edition)   Vol.J101-A   No.7   pp.189-195
Publication Date: 2018/07/01
Online ISSN: 1881-0195
Type of Manuscript: PAPER
discrete-time,  consensus,  pinning control,  multi-agent system,  

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In this paper, we consider the consensus problem of discrete-time multi-agent systems with a pinning control method. We select a single agent that is the root of a spanning tree as the pinning agent and consider a transfer function from the pinning input to the state of the pinning agent. Then using the root-locus method, we show that there exists an upper bound of the pinning gain to achieve the pinning consensus. With Gershgorin theorem, we show that under a certain assumption, root loci converging to zeros of the open-loop system always stay in the unit circle as the pinning gain increases from 0 to infinity.