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

Abstract EN

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.