Non-separation method-based finite-time synchronization of discrete-time fractional-order complex-valued neural networks with time-varying delays

In this paper, the finite-time synchronization (FTS) of discrete-time fractional-order complex-valued neural networks (FOCVNNs) with time-varying delays is studied using a non-separation method. In the literature, fractional-order Gronwall-type inequalities are typically used to analyze the FTS of fractional-order delayed systems, with the norm being estimated by an increasing function. However, for stable delay systems where the solution norm tends to zero, such estimations are not optimal. To improve the estimate for stable systems, a nabla Caputo difference inequality is first rigorously derived. Next, a delayed complex-valued adaptive nonlinear controller is designed, and a verifiable FTS criterion based on the established inequality is proposed, ensuring that the error norm is estimated by a decreasing function. Finally, numerical simulations are performed to validate the effectiveness of the proposed theoretical results.