Solvability condition for synchronization of discrete-time multi-agent systems and design

Antonie Arij Stoorvogel, Ali Saberi, Meirong Zhang, Zhenwei Liu

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


    This paper provides solvability conditions for state synchronization with homogeneous discrete-time multi-agent systems (MAS) with a directed and weighted communication network under full-state coupling. We assume only a lower bound for the second eigenvalue of the Laplacian matrices associated with the communication network is known. For the rest the weighted, directed graph is completely arbitrary. Our solvability conditions reveal that the synchronization problem is solvable for any nonzero lower bound if and only if the agents are at most weakly unstable (i.e., agents have all eigenvalues in the closed unit disc). However for a given lower bound, we can achieve synchronization for a class of unstable agents. We provide protocol design for at most weakly unstable agents based on either a direct eigenstructure assignment method or a standard H2 discrete-time algebraic Riccati equation (DARE). We also provide a protocol design for strictly unstable agents based on the standard H2 DARE.
    Original languageEnglish
    Title of host publicationAmerican Control Conference, ACC 2017
    Subtitle of host publicationSheraton Seattle Hotel, May 24-26, 2017, Seattle, USA
    ISBN (Electronic)978-1-5090-5992-8
    ISBN (Print)978-1-5090-4583-9
    Publication statusPublished - Jul 2017
    Event2017 American Control Conference, ACC 2017 - Seattle, United States
    Duration: 24 May 201726 May 2017


    Conference2017 American Control Conference, ACC 2017
    Abbreviated titleACC
    Country/TerritoryUnited States
    Internet address


    • Synchronization
    • Eigenvalues and eigenfunctions
    • Protocols
    • Couplings
    • Communication networks
    • Standards
    • Trajectory


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