Global asymptotic stability for octonion-valued neural networks with delay

Abstract

Over the last few years, neural networks with values in multidimensional domains have been intensely studied. This paper introduces octonion-valued neural networks with delay, for which the states and weights are octonions. The octonion algebra represents a non-associative normed division algebra which generalizes the complex and quaternion algebras and doesn’t fall into the category of Clifford algebras, which are associative. A sufficient criterion is derived in terms of linear matrix inequalities that ensures the existence, uniqueness, and global asymptotic stability of the equilibrium point for the proposed networks. Finally, a simulation example illustrates the effectiveness of the theoretical results.