Stability analysis for BAM quaternion-valued inertial neural networks with time delay via nonlinear measure approach

In this paper, the global stability for BAM quaternion-valued inertial neural networks with time delay is investigated without transforming the inertial terms into first order by some variable substitutions. To avoid the non-commutativity of quaternion multiplication, the discussed system is transformed into four real-valued models. Based on nonlinear measure approach and some inequality techniques, a new sufficient condition is obtained to ensure the existence and uniqueness of the equilibrium point. Meanwhile, some new Lyapunov functionals are constructed to directly propose the asymptotic stability for the discussed system and some new stability criteria in linear matrix inequality form are derived by means of Barbalat Lemma and inequality techniques. It is worth mentioning that this paper directly analyzes the dynamic performance of the concerned system, which is different from the traditional reduced-order variable replacement method. Finally, some numerical examples with simulations are given to demonstrate the validity of the theoretical results. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.