Exponential Finite-Time Consensus of Fractional-Order Multiagent Systems

The application of the fast sliding-mode control technique on solving consensus problems of fractional-order multiagent systems is investigated. The design and analysis are based on a combination of the distributed coordination theory and the knowledge of fractional-order dynamics. First, a sliding-mode manifold (surface) vector is defined, and then the fractional-order multiagent system is transformed into an integer-order (namely, first-order) multiagent system. Second, based on the fast sliding-mode control technique, a protocol is proposed for the obtained first-order multiagent system. Third, a new Lyapunov function is presented. By suitably estimating the derivative of the Lyapunov function, the reachability of the sliding-mode manifold is derived. It is proved that the exponential finite-time consensus can be achieved if the communication network has a directed spanning tree. Finally, the effectiveness of the proposed algorithms is demonstrated by some examples.