In this paper, we present the design for a decentralized control method comprising a series of local state feedback controllers for a class of linear fractional composite systems. In addition, the corresponding asymptotic stabilization criterion is derived. First, we design the local state feedback controllers for each subsystem of the linear fractional composite system. Then, based on the vector Lyapunov function, we combine these local state feedback controllers into a single decentralized controller through which the asymptotic stabilization criterion is proposed for the class of linear fractional composite system. Finally, numerical simulation of a class of linear fractional composite systems is used to verify the accuracy and effectiveness of the decentralized control method.

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