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Volume 5 Issue 6
Nov.  2018

IEEE/CAA Journal of Automatica Sinica

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Chi Huang, Guisheng Zhai and Gesheng Xu, "Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1044-1053, Nov. 2018. doi: 10.1109/JAS.2018.7511222
Citation: Chi Huang, Guisheng Zhai and Gesheng Xu, "Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1044-1053, Nov. 2018. doi: 10.1109/JAS.2018.7511222

Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems

doi: 10.1109/JAS.2018.7511222

Japan Ministry of Education, Sciences and Culture C21560471

the National Natural Science Foundation of China 61603268

the Research Project Supported by Shanxi Scholarship Council of China 2015-044

the Fundamental Research Project of Shanxi Province 2015021085

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  • We deal with a consensus control problem for a group of third order agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on weighted difference between its states and those of its neighbor agents, we aim to propose an algorithm on computing the weighting coefficients in the control input. The problem is reduced to designing Hurwitz polynomials with real or complex coefficients. We show that by using Hurwitz polynomials with complex coefficients, a necessary and sufficient condition can be obtained for designing the consensus algorithm. Since the condition is both necessary and sufficient, we provide a kind of parametrization for all the weighting coefficients achieving consensus. Moreover, the condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively decreased computation burden. The result is also extended to the case where communication delay exists in the control input.


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