Exponential stability for delayed octonion-valued recurrent neural networks

Abstract

Over the last few years, neural networks with values in multidimensional domains have gained a lot of interest. A non-associative normed division algebra which generalizes the complex and quaternion algebras is represented by the octonion algebra. It does not fall into the category of Clifford algebras, which are associative. Delayed octonionvalued recurrent neural networks are introduced, for which the states and weights are octonions. A sufficient criterion is given in the form of linear matrix inequalities, which assures the global exponential stability of the equilibrium point for the proposed networks. Lastly, a numerical example illustrates the correctness of the theoretical results.