Quantized $ \mathcal{H}_\infty $ synchronization for Hopfield networks subject to time-variable delay
Tianran Bu · Networks and Heterogeneous Media · 2025
This paper is dedicated to the study of $ \mathcal{H}_\infty $ synchronization for Hopfield networks (HNs) with time-variable delay via quantized control. The delay function is assumed to be continuous and bounded, yet not necessarily differentiable. A delay-dependent sufficient condition is derived using a linear combination of Lyapunov functional candidates along with two matrix inequalities to ensure the $ \mathcal{H}_\infty $ synchronization of drive-response HNs. Based on this, an alternative sufficient condition characterized by reduced nonlinearities is further established by employing decoupling techniques. With fixed bounds on the time delay and the $ \mathcal{H}_\infty $ disturbance attenuation level, an algorithm is then proposed to compute the minimum required gain for the quantized controller. Finally, a numerical example demonstrates the effectiveness of the proposed $ \mathcal{H}_\infty $ synchronization results.