Chaos, Solitons and Fractals 115 (2018) 268–282 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos Novel results on passivity and exponential passivity for multiple discrete delayed neutral-type neural networks with leakage and distributed time-delays C. Maharajan a , R. Raja b , Jinde Cao c,∗ , G. Rajchakit d , Ahmed Alsaedi e 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 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia a r t i c l e i n f o Article history: Received 12 September 2017 Revised 2 March 2018 Accepted 9 July 2018 Keywords: Neural networks Lyapunov-Krasovskii functional Passivity Neutral-type neural networks Linear matrix inequality Exponential passivity Distributed time-delays Multiple discrete delays Neutral delays Leakage delays a b s t r a c t This paper investigates the problem of passivity and exponential passivity for neutral-type neural net- works (NNNs) with leakage, multiple discrete delay and distributed time-delay, via some novel suffi- cient conditions. Based on an appropriate Lyapunov-Krasovskii functional (LKF), free weighting matrix approach and some inequality techniques, enhanced passivity criteria for the concerned neural networks is established in the form of Linear matrix inequalities (LMIs). The feasibility of the attained passivity and exponential passivity criterions easily verified by the aid of LMI control toolbox in MATLAB software. Furthermore, we have compared our method with previous one in the existing literature, which depicts its less conservativeness. To substantiate the superiority and effectiveness of our analytical design, two examples with their numerical simulations are provided. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction In current scenario, extensive attention has been paid on neu- ral networks (NNs) due to their fruitful applications in many fields, such as intelligent robot, signal processing, associative memories, fixed-point computations, automatic control, artificial intelligence, and so on [13,16,34,44]. It is well known that the time delays of- ten occur from finite switching speed of the communication time, amplifiers and faults in the electrical circuits when the imple- mentation of neural networks. Thus, the existence of time delays is inevitable in dynamical systems, which may affects the pas- siveness generating instability, bad performance, chaotic behavior ∗ Corresponding author. This work was jointly supported by the Rajiv Gandhi National Fellowship under the University Grant Commission, New Delhi with (Ref. No.F1-17.1/2016-17/RGNF-2015-17-SC-TAM-21509), the Jiangsu Provincial Key Labo- ratory of Networked Collective Intelligence under Grant No. BM2017002, and the Thailand research grant fund (RSA5980019) and Maejo University. E-mail address: jdcao@seu.edu.cn (J. Cao). and swinging or oscillation. Hence, the study on neural networks with time-delays have been considerable attention from many re- searchers, see for references [6,31,36]. In [43,46], the authors inves- tigates the passivity criteria for time delayed neural networks with the help of LKF. In accordance, the delay-dependent and delay-independent cri- teria are two categories of time delays in neural networks, which classified by the existing time delayed results. So far as, one can observe from available literatures, the delay-dependent case is less conserved than the delay independent ones. Further, time delay can be characterized into two types: a Discrete and Distributed de- lays. Here, we have taken both time delays, that is multiple dis- crete time delays and the distributed delays, into account while model our network system, because the length of the axon sizes are too large. For sequence, the passivity of various classes of neu- ral networks with time delay has become an interesting area and different passivity conditions have been established for such NNs for multiple delays [53,57] and distributed time-delays [8,23,63]. As a result, it is noteworthy to inspect both the time-delay https://doi.org/10.1016/j.chaos.2018.07.008 0960-0779/© 2018 Elsevier Ltd. All rights reserved.