Sliding-Mode Synchronization Control of Complex-Valued Inertial Neural Networks With Leakage Delay and Time-Varying Delays

This work explores the synchronization problem of two nonidentical complex-valued inertial neural networks (CVINNs) considering time-varying delays, leakage delay, and external disturbances. The entire analysis does not use reduced-order conversion, nor does it involve the separation of real and imaginary parts, but directly focuses on the original system. First, an integral sliding-mode surface suitable for the system is proposed. Second, the efficient sliding-mode control laws are designed, under which the state trajectories of the closed-loop dynamic error systems can be driven onto the predefined sliding-mode surface in finite time. Then, not requiring the time-varying delays to be differentiable, by constructing innovative Lyapunov-Krasovskii functionals, the synchronization criteria are obtained in the forms of the linear matrix inequality techniques. Eventually, for the systems with different types of activation functions, the corresponding numerical verification and comparison are carried out.