Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks

This article investigates the problem of finite-time synchronization of fractional-order complex-valued random multi-layer networks without decomposing them into two real-valued systems. Firstly, by promoting real-valued signum functions, sign functions on the complex-valued domain are introduced. Simultaneously, quantization functions in the complex-valued domain are also introduced, and several related formulas for sign functions and quantization functions in complex-valued domain are established. Under the framework of the given sign function and quantization function, an adaptive quantized control scheme with or without deception attacks is designed. According to the finite-time theorem, Lyapunov function, and graph theory methods, some sufficient criteria for realizing finite-time synchronization in complex-valued fractional-order multi-layer networks have been obtained. Furthermore, the setting time of finite-time synchronization is effectively evaluated. Eventually, the reliability of our results and the practicality of control strategies are verified through numerical examples.