Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

This chapter addresses the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on complex networks without strong connectedness by employing fractional sliding mode control (SMC). By integrating the hierarchical algorithm with graph theory, a novel SMC strategy is devised to achieve projective synchronization between the master and slave systems. This strategy encompasses both global complete synchronization and global antisynchronization, thereby providing a comprehensive solution for various synchronization scenarios. Additionally, new criteria are derived to ensure the Mittag-Leffler stability of the projective synchronization error system, offering robust theoretical guarantees for the proposed approach. Finally, a numerical example is provided to demonstrate the validity and effectiveness of the proposed method, highlighting its potential applications in complex network systems and its superiority in handling fractional-order dynamics.