Applied Mathematics and Computation 326 (2018) 33–55 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: A non-fragile state estimation approach C. Maharajan a , R. Raja b , Jinde Cao c,∗ , G. Rajchakit d , Zhengwen Tu e , Ahmed Alsaedi f a Department of Mathematics, Alagappa University, Karaikudi 630 004, India b Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India c School of Mathematics, Southeast University, Nanjing 211189, China d Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand e School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China f Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia a r t i c l e i n f o Keywords: Exponential stability Lyapunov–Krasovskii functional BAM-type neural networks Linear matrix inequality Non-fragile state estimator a b s t r a c t In this epigrammatic, the problem of exponential stability for BAM-type neural networks (BAMNNs) with non-fragile state estimator is investigated under time-varying delays. The delays in discrete and distributed terms are assumed to be time-varying, which means that the lower and upper bounds can be derived. Without involving the time-delays or the activation functions, the non-fragile estimators are constructed in terms of simple linear formation and also the implementation of state estimators are uncomplicated. In addition, the non-fragile estimators are reduced the possible implementation errors in neural net- works. For consequence, reason of energy saving, the non-fragile estimators are designed with neural networks. By fabricating a suitable LKF (Lyapunov–Krasovskii functional) and enroling some analysis techniques, a novel sufficient conditions for exponential stability of the designated neural networks are derived in terms of Linear Matrix Inequalities (LMIs), which can be easily assessed by MATLAB LMI Control toolbox. Accordingly, the research proposed here, is advanced and less conservative than the previous one exists in the liter- ature. Finally, two numerical examples with simulations and comparative studies are per- formed to substantiate the advantage and validity of our theoretical findings. © 2018 Elsevier Inc. All rights reserved. 1. Introduction Recently, the study on neural networks (NNs) in dynamical behaviors has received considerable attention due to their potential applications in different fields, such as robot signal processing, automatic control, static image treatment, optimization problems, parallel computing, signal processing, etc [4,12,18,24]. In particular, bidirectional associative memory (BAM) neural networks is a special type of recurrent NNs, which was coined by Kosko [22,23]. A BAM neural networks is ∗ Corresponding author. E-mail address: jdcao@seu.edu.cn (J. Cao). https://doi.org/10.1016/j.amc.2018.01.001 0096-3003/© 2018 Elsevier Inc. All rights reserved.