Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method

Abstract

This paper concentrates on the robust stability of uncertain parameter quaternionic neural networks (QNNs) with both time-varying delays and infinite distributed delays. To this end, a derivative formula of quaternionic function’s norm is firstly established. Then, based on this formula, algebraic standards are obtained by employing M-matrix theory as well as analytical techniques to guarantee the global robust exponential stability of the considered QNNs. Particularly, different from most existing decomposition approaches, this whole quaternionic method can be used whether the QNNs are decomposable or not and greatly reduces computation cost. The utility of the easy-to-use results formulated in the form of quaternionic norm’s M-matrix is confirmed by three given instances with numerical simulation.