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Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay

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  • Jun Liu
  • Wei Chen
  • Kaiyu Qin
  • Ping Li

Abstract

This paper is devoted to the consensus problems for a fractional-order multiagent system (FOMAS) with double integral and time delay, the dynamics of which are double-integrator fractional-order model, where there are two state variables in each agent. The consensus problems are investigated for two types of the double-integrator FOMAS with time delay: the double-integrator FOMAS with time delay whose network topology is undirected topology and the double-integrator FOMAS with time delay whose network topology is directed topology with a spanning tree in this paper. Based on graph theory, Laplace transform, and frequency-domain theory of the fractional-order operator, two maximum tolerable delays are obtained to ensure that the two types of the double-integrator FOMAS with time delay can asymptotically reach consensus. Furthermore, it is proven that the results are also suitable for integer-order dynamical model. Finally, the relationship between the speed of convergence and time delay is revealed, and simulation results are presented as a proof of concept.

Suggested Citation

  • Jun Liu & Wei Chen & Kaiyu Qin & Ping Li, 2018. "Consensus of Fractional-Order Multiagent Systems with Double Integral and Time Delay," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, May.
    • Handle: RePEc:hin:jnlmpe:6059574
    DOI: 10.1155/2018/6059574
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