Abstract
In this paper, several consensus problems are studied for fractional-order double-integrator multi-agent systems, where the order of fractional derivative belongs to (0, 1). Both continuous-time and sampled-data based consensus protocols are proposed for absolute and relative damping cases, respectively. For the continuous-time protocols, consensus is achieved by using the connection between integer-order and fractional-order multi-agent systems. For the sampled-data based protocols, convergence analysis is provided by using the Hermite–Biehler theorem, which is used to deal with the stability of a polynomial with complex coefficients. It is shown that the consensus value is a function of the initial conditions for the absolute damping case, while the consensus value is related to the initial conditions and the time for the relative damping case. In addition, some examples are provided to validate the correctness of the main theorems.
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