Novel Heterogeneous Mode-Dependent Impulsive Synchronization for Piecewise T-S Fuzzy Probabilistic Coupled Delayed Neural Networks

This article investigates the heterogeneous impulsive synchronization for T-S fuzzy probabilistic coupled delayed neural networks (CDNNs) with mode-dependent parameters and piecewise membership functions. To begin with, a novel CDNNs model with adjustable coupling strength and probabilistic coupling delays is designed to ensure the accuracy of the CDNNs model. Meanwhile, the generalized isolated node with four types of mismatched parameters, named heterogeneous isolated delayed neural network, is first considered to extend the synchronization problem. Then, the mode-dependent fuzzy rules are introduced to design the novel model, which implies that switching signals and fuzzy processes are interdependent and can share information to communicate. To improve the hybrid controller's reliability, the mode-dependent impulses are also developed here, in which the impulsive effects with different properties can occur at any moment in the switching interval. The exponential synchronization conditions are derived by means of the method of auxiliary state variables, Lyapunov–Krasovskii functional, average switching dwell period, and mode-dependent average impulsive dwell period. Moreover, the improved mode-dependent piecewise approximated membership functions are proposed to reduce the main results' conservatism. Finally, a numerical example is provided to illustrate the effectiveness of the main results.