Robust stability analysis of quaternion-valued neural networks with time delays and parameter uncertainties

Abstract

This paper addresses the problem of robust stability for quaternion-valued neural networks (QVNNs) with leakage delay, discrete delay and parameter uncertainties. Based on Homeomorphic mapping theorem and Lyapunov theorem, via modulus inequality technique of quaternions, some sufficient conditions on the existence, uniqueness, and global robust stability of the equilibrium point are derived for the delayed QVNNs with parameter uncertainties. Furthermore, as direct applications of these results, several sufficient conditions are obtained for checking the global robust stability of QVNNs without leakage delay as well as complex-valued neural networks (CVNNs) with both leakage and discrete delays. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.