This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

本文考虑了分数阶滑模控制（SMC）在没有强连通性的复杂网络上分数阶耦合系统（FOCS）的Mittag-Leffler投影同步问题。将层次算法与图论相结合，设计了一种新的SMC策略来实现主系统与从系统之间的投影同步，该策略涵盖了全局完全同步和全局反同步。此外，推导了一些新颖的准则来保证投影同步误差系统的Mittag-Leffler稳定性。最后，通过算例说明了该方法的有效性。