Settling-Time Estimation for Finite-Time Stabilization of Fractional-Order Quaternion-Valued Fuzzy NNs

This article solves the problems of finite-time control and settling-time estimation for fractional-order quaternion-valued fuzzy neural networks (FQFNNs) with time delays. A novel fractional differential inequality is established to estimate the settling time of the addressed system, which is more general and less conservative than the existing results. In addition, owing to the noncommutativity of multiplication of quaternions, the decomposition method is usually adopted to discuss the finite-time stabilization (FTS) of quaternion-valued neural networks, which inevitably doubles the dimensionality of the system and brings a great computational burden. To avoid the aforementioned issues, some new properties of the quaternion-valued signum function are presented for exploring the FTS of FQFNNs by the direct quaternion method without any decomposition. Then, 1-norm and 2-norm control strategies are designed to stabilize the addressed system in finite time, and several sufficient criteria are derived to ensure the FTS of FQFNNs. Finally, the validity of the obtained theoretical results and the superiority of the proposed estimation method are illustrated by numerical simulations.