Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

A state-derivative feedback (SDF) is added into the designed control protocol in the existing paper to enhance the robustness of a fractional-order multiagent system (FMS) against nonuniform time delays in this paper. By applying the graph theory and the frequency-domain analysis theory, consensus conditions are derived to make the delayed FMS based on state-derivative feedback reach consensus. Compared with the consensus control protocol designed in the existing paper, the proposed SDF control protocol with nonuniform time delays can make the FMS with SDF and nonuniform time delays tolerate longer time delays, which means that the convergence speed of states of the delayed FMS with SDF is accelerated indirectly. Finally, the corresponding results of simulation are given to verify the feasibility of our theoretical results.

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 doubleintegrator 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.

Consensus of fractional-order multiagent systems (FOMASs) with single integral has been wildly studied. However, the dynamics with multiple integral (especially double integral to sextuple integral) also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems (MIFOMASs) with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results.