Abstract
In this paper, a model of discrete delayed quaternion-valued neural networks with interval parameter uncertainties is considered. Some sufficient conditions for the existence, uniqueness and globally robust stability of the equilibrium point are obtained. The approach is on the basis of the homeomorphic mapping method, the Lyapunov stability theorem and inequality techniques. Finally, a numerical example is given to demonstrate the application of the obtained results.
Highlights
1 Introduction Since neural networks had been proposed in the 1940s, they have been widely studied by many researchers, due to the many applications in various areas, such as associative memory, optimization, pattern recognition, fault diagnosis and signal processing
3 Global robust stability results we will present the existence and uniqueness of the equilibrium point of the delayed quaternion-valued neural networks (QVNNs) on the basis of Assumptions (A1) and (A2), we investigate the global robust stability of the equilibrium point of the delayed QVNNs
We would like to point out that more quaternion-valued neural networks can be generalized based on our main results such as discrete-time neural networks [26], stochastic perturbations [37], and Markovian jumping parameters [38]
Summary
Since neural networks had been proposed in the 1940s, they have been widely studied by many researchers, due to the many applications in various areas, such as associative memory, optimization, pattern recognition, fault diagnosis and signal processing. Some authors have considered the existence, uniqueness and global stability of the equilibrium point for delayed quaternion-valued neural networks [14, 26,27,28,29,30,31,32,33,34]. The work above is very excellent, little research considered robust stability of quaternion-valued neural networks with delay and interval parameter uncertainties. Chen in [35, 36] considered the robust stability with different kinds of delays for quaternion-valued neural networks, some sufficient conditions have been obtained about the existence, uniqueness and global asymptotic robust stability.
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