Passivity and State Estimation for Quaternion-Valued Neural Networks with Two Additive Delays

This paper investigates the finite-time passivity and state estimation problem for quaternion-valued neural networks with two additive delays. By employing the Lyapunov method, several criteria are derived to ensure the finite-time passivity of the discussed system and the asymptotic stability of the error system. A novel controller is proposed to achieve finite-time passivity of the discussed system and a proportional–integral observer (PIO) strategy is adopted to tackle the state estimation problem. The direct approach is used to handle the quaternion-valued neural networks without decomposing them into real-valued or complex-valued systems, which substantially simplifies the analysis procedure. Moreover, various quaternion-valued inequalities are utilized in the analysis, contributing to reduced conservatism in the derived results. Finally, the theoretical results have been effectively demonstrated through two numerical simulation examples.