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Volume 11 Issue 4
Apr.  2024

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2024  >  11(4): 878-892
H. Wang and  Q.-L. Han,  “Designing proportional-integral consensus protocols for second-order multi-agent systems using delayed and memorized state information,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 878–892, Apr. 2024. doi: 10.1109/JAS.2024.124308
Citation: H. Wang and  Q.-L. Han,  “Designing proportional-integral consensus protocols for second-order multi-agent systems using delayed and memorized state information,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 878–892, Apr. 2024. doi: 10.1109/JAS.2024.124308
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Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

doi: 10.1109/JAS.2024.124308
Funds:  This work was supported in part by the National Natural Science Foundation of China (NSFC) (61703086, 61773106) and the IAPI Fundamental Research Funds (2018ZCX27)
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    Abstract

  • This paper is concerned with consensus of a second-order linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network. A proportional-integral consensus protocol is designed by using delayed and memorized state information. Under the proportional-integral consensus protocol, the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system. Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system, but also plays a critical role in the dynamic performance of the system. In this paper, based on recent results on the distribution of roots of quasi-polynomials, several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived. Then allowable regions of consensus protocol parameters are estimated. Some necessary and sufficient conditions for determining effective protocol parameters are provided. The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system. Moreover, the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated. Furthermore, some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

     

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    Highlights

    • New results on Hurwitz stability for a class of quasi-polynomials
    • Consensus design for LTI multi-agent systems via eigenvalue assignment
    • Improving the dynamic performance in addition to achieving the consensus
    • Analysis about effects of delays on consensus of harmonic oscillators/double integrators

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