Distributed consensus tracking for the fractional-order multi-agent systems based on the sliding mode control method

Distributed consensus tracking for the fractional-order multi-agent systems is mainly studied in this paper. Firstly, the simple Lyapunov candidate function is discussed to judge the validity of the proposed controller. Secondly, according to the sliding mode control method, a controller is designed to achieve the consensus tracking problem when the followers are described by the fractional-order linear dynamics. Thirdly, the case when the dynamics of followers own the intrinsic nonlinear function is discussed, it proves that the designed sliding mode controller is still valid for this case under the certain conditions. For the above two parts, the systems stabilities are judged based on the result of the first part. Finally, several simulations are presented to verify the obtained results.