Finite time cluster consensus of fractional-order multi-agent systems with directed topology

Abstract

In this paper, the finite time cluster consensus (FnTCC) of fractional-order multi-agent systems (FOMAS) with directed topology is investigated. The fractional-order system is converted into an integer-order system by defining a neighborhood-based error variable, and suitable control rules are designed for the obtained first-order multi-agent system. According to the exponential finite-time stability theorem, suitable Lyapunov functions are designed. Furthermore, the settling time function is given. Numerical simulation results prove the feasibility and validity of our theory.