Bipartite Synchronization of Fractional-Order Multi-Layer Signed Network With a Non-Autonomous Leader

This article investigates the problem of bipartite synchronization with a non-autonomous leader in fractional-order multi-layer signed network. To address the chattering phenomenon induced by the use of sign functions in existing studies for mitigating the influence of bounded unknown leader inputs, a continuous controller and a dynamic event-triggered controller are proposed, respectively. The continuous controller is introduced a decay function to ensure the continuity of the control input, thereby effectively avoids chattering. The dynamic event-triggered controller leverages the characteristics of event-triggered control, the input remains constant within triggered intervals, which confines discontinuities to discrete triggering instants. This approach not only eliminates chattering but also reduces the frequency of control updates. Besides, the measurement error is designed by synchronization error and introduce a new trigger mechanism, avoiding the issue of the existence of the fractional-order right-Dini derivative at zero caused by measurement error designed through the controller with the sign function. Notably, the controllers proposed in this paper are not only applicable to non-autonomous systems but also to those subject to external disturbances as well as traditional autonomous leader systems. The stability of the error system is demonstrated by Lyapunov method. In the end, the proposed corollaries and theorems are verified by three simulations.