Exponential Stability of Discrete-Time Cellular Uncertain BAM Neural Networks with Variable Delays using Halanay-Type Inequality

Authors

C. Sowmiya, Department of Mathematics, Alagappa University, Karaikudi-630 004, India.Follow
R. Raja, Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi-630 004, India.Follow
Jinde Cao, Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, School of Mathematics, Southeast University, Nanjing 211189, China.Follow
G. Rajchakit, Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand.Follow
Ahmed Alsaedi, Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.Follow

Author Country (or Countries)

India.

Abstract

This paper is concerned with the class of uncertain discrete time Bi-directional associative memory (BAM) cellular neural networks with variable delays. Here the result is enhanced to ensure the global stability in the sense of exponential for the addressed time delayed neural networks by employing a discrete analogue of Halanay-type inequality. This type of inequalities can be used as basic tool in the study of exponential stability of the equilibrium for certain generalized difference equations. An important feature presents in our paper is that, with the help of time-invariant perturbation matrix which is often called parameter uncertainties, the proposed stability conditions can be proved. [(i.e) It is allowed to be norm-bounded]. At last, three illustrative examples with simulations are provided for the addressed neural networks to demonstrate the usefulness and flexibility of the proposed design approach.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/journal/100309

Recommended Citation

Sowmiya, C.; Raja, R.; Cao, Jinde; Rajchakit, G.; and Alsaedi, Ahmed (2018) "Exponential Stability of Discrete-Time Cellular Uncertain BAM Neural Networks with Variable Delays using Halanay-Type Inequality," Applied Mathematics & Information Sciences: Vol. 12: Iss. 3, Article 9.
DOI: http://dx.doi.org/10.18576/journal/100309
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss3/9