Fixed-Time Consensus of Fractional-Order Single Integrator Multi-Agent Systems

The problem of consensus in fractional order single-integrator multi-agent systems has been studied in this paper. The effect of memory is considered using the Riemann-Liouville fractional derivative in the dynamics of the agents. In order to achieve convergence among the agents, a fractional order control protocol based on the error signal between neighboring agents is proposed. Using Lyapunov's stability theorem, a Lyapunov function is introduced that shows that the agents converge over a specified settling time and the upper bound of the settling time is obtained. The merit of the proposed bound for the settling time is that it is independent of the initial conditions. Finally, some simulations are provided to confirm the introduced method.