Abstract
This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.
Highlights
Neural networks (NNs) operate on principles similar to the human nervous system
By using the Frobenius norm, we prove a new sufficient condition for existence of equilibrium point of our NNs model (2) which is unique
Global stability of NNs has been studied by using the Frobenius norm result under parameter uncertainties
Summary
Neural networks (NNs) operate on principles similar to the human nervous system. It has a huge number of processors. Erefore, the GARS analysis of NNs under parameter uncertainties is the most important problem It has been exclusively studied by many authors in [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. E objective of this paper is to obtain a new sufficient condition for the GARS of the equilibrium point of the delayed neural system using the Lyapunov stability theory and Frobenius norm under parameter uncertainties. Erefore, the Frobenius norm is important for calculating the upper bound of connection weight matrices. En, H < S implies that wTHw < wTSw for any real vector w (w1, w2, . . . , wn)T
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