Delay consensus of fractional-order multi-agent systems with sampling delays

In the complex practical environments, many distributed multi-agent systems can not be described with the integer-order dynamics and can only be illustrated with the fractional-order dynamics. In this paper, consensus problems of discrete-time networked fractional-order multi-agent systems with sampling delay are investigated. Firstly, the collaborative control of discrete-time multi-agent systems with fractional-order operator is analyzed in a directed network ignoring sampling delay by using Laplace transform and frequency domain. Then, by applying Hermit-Biehler theorem, the consensus of fractional-order multi-agent systems with sampling delay is studied in a misdirected network. A number of consensus conditions for fractional-order systems with sampling delay are obtained. Numerical simulations are shown to illustrate the utility of the theoretical results.