Parameter-range-dependent robust stability conditions for quaternion-valued neural networks with time delays

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.

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

“…In [25,27], the influence of leakage and discrete delays on CVNNs are studied. In [28], the effects of leakage and discrete delays in QVNNs are considered. To the best of our knowledge, the results of QVNNs with leakage, discrete, and distributed delays are few.…”

“…But in its judging criteria, two negative definite matrices are needed, and the terms in these matrices are the maximum values, which are determined by the absolute values of the upper and lower bounds of the elements of the connection weight matrix, ignoring the sign of the connection weight value. To overcome this shortcoming, Wang in [28] revisited the system and obtained a criterion whose elements rely on both the lower and upper bounds of the interval parameters.…”

“…By means of quaternion-valued inequality, Lyapunov function, and homeomorphic mapping, a new sufficient condition to ensure the existence, uniqueness, and global robust stability of an equilibrium point for the QVNN is derived, which can be checked numerically using the effective YALMIP toolbox in MATLAB. Comparing to other references, our contributions lie in two aspects: firstly, the traditional model is extended in the article, the distributed delay and impulsive effect are considered in our model, which make the model more practical and is the substantial extension of the study of [8,28], because the existence of the distributed delay and impulsive effect increases the dimension of the system, which produces great difficulties in numerical simulation and for the proof of the negative definiteness for V function. Secondly, in the judging criteria of reference [13,36], the negative definiteness of two matrices is needed, however, in this paper, only one negative definite judging matrix is enough to guarantee the existence, uniqueness, and global robust stability of the equilibrium point.…”