Distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays.

• The dynamic model for distributed formation control of double-integrator fractional-order multi-agent systems is established. • The formation control protocol for distributed formation control of double-integrator fractional-order multi-agent systems is proposed. • Two delay margins are derived to achieve distributed formation control of double-integrator fractional-order multi-agent systems with relative damping and nonuniform time-delays. • Two numerical simulation results are given to demonstrate the validity of our theoretical analysis. In this paper, distributed formation control problems are studied for double-integrator fractional-order multi-agent systems (DIFOMASs) with relative damping and nonuniform time-delays. The required state deviations of a group of multi-agent systems are achieved through a local state information interaction, which means that this group of multi-agent systems achieves formation control. In the context of this paper, the dynamic model is first established and the formation control protocol is designed for distributed formation control of DIFOMASs with relative damping under symmetric time-delays and asymmetric time-delays. Then, some sufficient conditions for achieving distributed formation control of DIFOMASs are acquired with the help of graph theory, matrix theory, stability theory and frequency-domain theory. In the end, two simulation examples are performed to verify the efficacy of our proposed method. [ABSTRACT FROM AUTHOR]