Sampled-data global exponential synchronization of multi-delay fuzzy inertial neural networks

This study investigates the attainment of global exponential synchronization (GES) in fuzzy inertial neural networks (FINNs) that incorporate time-varying leakage, transmission and distributed delays. The study utilizes a sampled-data control approach for system design. First of all, the considered FINNs incorporate both inertial and fuzzy components. From a technical perspective, the speed at which cellular neuronal signals are transmitted and processed can be effectively represented using a first-order differential equation. However, the network’s reaction to incoming information often exhibits time-dependent characteristics, which are better captured by a second-order inertial neural network framework. Fuzzy logic systems utilize input-output frameworks structured through product-sum operations, enabling rule-based assessment of data transfer processes. Introducing fuzzy terms helps to minimize ambiguity and uncertainty effectively. Subsequently, a novel parameterized-solution-based direct analysis method is proposed, which avoids the necessity of variable substitution or the use of Lyapunov–Krasovskii functionals (LFs), thereby simplifying the theoretical derivation and reducing the computational workload. Moreover, based on this method, a new GES criterion is obtained for the FINNs system with multiple time delays. Compared with the GES conditions obtained by other methods, this criterion only contains a few simple inequalities and is easier to be checked. Finally, the efficacy of this proposed theoretical findings is validated through a numerical example.