Novel Halanay Inequality-Based Reachable Set Estimation for Complex-Valued Memristive Fuzzy Neural Networks With Proportional Delays.

This brief investigates the reachable set estimation (RSE) for a class of uncertain complex-valued memristive Takagi-Sugeno (T-S) fuzzy neural networks (MTSFNNs) with proportional delays. It presents the first study of RSE for neural networks (NNs) with unbounded delay. By leveraging the properties of proportional delay and polynomial functions, a novel Halanay inequality is established and extended to proportional delay NNs. Furthermore, a numerical example under both zero and nonzero initial conditions validates the proposed approach, achieving a tighter over-approximation of the reachable set via quantum particle swarm optimization (QPSO).