Robust exponential stability of non-deterministic fuzzy neural networks: A global unidirectional quaternary implicit criterion

This paper provides a sufficient criterion for robust global exponential stability (RGES) of non-deterministic fuzzy neural networks (NDFNNs), where “non-deterministic” feature maps the effect of the variability of piecewise constant argument (PCAs), derivative term coefficients (DTCs) and twofold uncertain connection weights.To determine the supremum of the non-deterministic parameters, an algorithm for the global unidirectional sequential calculation is designed, including the feasible domain of the connection weight intensities that interfere with the transient performance of NDFNNs. Furthermore, the existence and uniqueness of the solution of NDFNNs are further elucidated. These are achieved by solving quaternary implicit transcendental equations utilizing Gronwall inequality. Compared to previous results, an additional geometric representation of the allowable intensity of connection weights is provided, accounting for the influence of PCAs and DTCs, is given. The designed algorithm based on unidirectional quaternary implicit criterion fully considers the sequential relation of update process. Specifically, the unidirectional algorithm enables the supremum of subsequent elements to depend on previously computed ones, creating a coupled relationship and enhancing accuracy. Finally, the validity of the theoretical results for ensuring the RGES of NDFNNs is illustrated by the simulation cases.