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Ding Z, Yang L, Ye Y, Li S, Huang Z. Passivity and passification of fractional-order memristive neural networks with time delays. ISA TRANSACTIONS 2023; 137:314-322. [PMID: 36746695 DOI: 10.1016/j.isatra.2023.01.034] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Revised: 12/23/2022] [Accepted: 01/27/2023] [Indexed: 06/04/2023]
Abstract
A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.
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Affiliation(s)
- Zhixia Ding
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Le Yang
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Yanyan Ye
- School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Sai Li
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Zixin Huang
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
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Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays. MATHEMATICS 2021. [DOI: 10.3390/math9243321] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient conditions for finite boundness, finite-time stability and finite-time passivity, which has never been performed before. First, we create a new Lyapunov–Krasovskii functional, Peng–Park’s integral inequality, descriptor model transformation and zero equation use, and then we use Wirtinger’s integral inequality technique. New finite-time stability necessary conditions are constructed in terms of linear matrix inequalities in order to guarantee finite-time stability for the system. Finally, numerical examples are presented to demonstrate the result’s effectiveness. Moreover, our proposed criteria are less conservative than prior studies in terms of larger time-delay bounds.
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Cao Y, Wang S, Guo Z, Huang T, Wen S. Event-based passification of delayed memristive neural networks. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.03.045] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Guo Z, Wang S, Wang J. Global Exponential Synchronization of Coupled Delayed Memristive Neural Networks With Reaction-Diffusion Terms via Distributed Pinning Controls. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:105-116. [PMID: 32191900 DOI: 10.1109/tnnls.2020.2977099] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article presents new theoretical results on global exponential synchronization of nonlinear coupled delayed memristive neural networks with reaction-diffusion terms and Dirichlet boundary conditions. First, a state-dependent memristive neural network model is introduced in terms of coupled partial differential equations. Next, two control schemes are introduced: distributed state feedback pinning control and distributed impulsive pinning control. A salient feature of these two pinning control schemes is that only partial information on the neighbors of pinned nodes is needed. By utilizing the Lyapunov stability theorem and Divergence theorem, sufficient criteria are derived to ascertain the global exponential synchronization of coupled neural networks via the two pining control schemes. Finally, two illustrative examples are elaborated to substantiate the theoretical results and demonstrate the advantages and disadvantages of the two control schemes.
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Yu Y, Wang X, Zhong S, Yang N, Tashi N. Extended Robust Exponential Stability of Fuzzy Switched Memristive Inertial Neural Networks With Time-Varying Delays on Mode-Dependent Destabilizing Impulsive Control Protocol. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:308-321. [PMID: 32217485 DOI: 10.1109/tnnls.2020.2978542] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article investigates the problem of robust exponential stability of fuzzy switched memristive inertial neural networks (FSMINNs) with time-varying delays on mode-dependent destabilizing impulsive control protocol. The memristive model presented here is treated as a switched system rather than employing the theory of differential inclusion and set-value map. To optimize the robust exponentially stable process and reduce the cost of time, hybrid mode-dependent destabilizing impulsive and adaptive feedback controllers are simultaneously applied to stabilize FSMINNs. In the new model, the multiple impulsive effects exist between two switched modes, and the multiple switched effects may also occur between two impulsive instants. Based on switched analysis techniques, the Takagi-Sugeno (T-S) fuzzy method, and the average dwell time, extended robust exponential stability conditions are derived. Finally, simulation is provided to illustrate the effectiveness of the results.
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Wang JL, Qiu SH, Chen WZ, Wu HN, Huang T. Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:5231-5244. [PMID: 32175875 DOI: 10.1109/tnnls.2020.2964843] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.
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Rajchakit G, Chanthorn P, Niezabitowski M, Raja R, Baleanu D, Pratap A. Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.07.036] [Citation(s) in RCA: 44] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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9
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Exponential synchronization of complex-valued memristor-based delayed neural networks via quantized intermittent control. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.04.097] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Duan L, Wang Q, Wei H, Wang Z. Multi-type synchronization dynamics of delayed reaction-diffusion recurrent neural networks with discontinuous activations. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.040] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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11
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Ren J, Song Q, Gao Y, Lu G. Leader-following bipartite consensus of second-order time-delay nonlinear multi-agent systems with event-triggered pinning control under signed digraph. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.043] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Yue CX, Wang L, Hu X, Tang HA, Duan S. Pinning control for passivity and synchronization of coupled memristive reaction–diffusion neural networks with time-varying delay. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.09.103] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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You X, Song Q, Zhao Z. Existence and finite-time stability of discrete fractional-order complex-valued neural networks with time delays. Neural Netw 2020; 123:248-260. [DOI: 10.1016/j.neunet.2019.12.012] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2019] [Revised: 11/28/2019] [Accepted: 12/10/2019] [Indexed: 10/25/2022]
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14
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Global Mittag-Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delay. Neural Netw 2020; 122:382-394. [DOI: 10.1016/j.neunet.2019.11.004] [Citation(s) in RCA: 44] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Revised: 10/06/2019] [Accepted: 11/04/2019] [Indexed: 11/21/2022]
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Xiao J, Wen S, Yang X, Zhong S. New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality. Neural Netw 2020; 122:320-337. [DOI: 10.1016/j.neunet.2019.10.017] [Citation(s) in RCA: 66] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 09/10/2019] [Accepted: 10/28/2019] [Indexed: 11/16/2022]
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16
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Xiao J, Zhong S. Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.06.044] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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18
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Xiong W, Yu X, Patel R, Huang T. Stability of Singular Discrete-Time Neural Networks With State-Dependent Coefficients and Run-to-Run Control Strategies. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:6415-6420. [PMID: 29994546 DOI: 10.1109/tnnls.2018.2829172] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this brief, sustaining and intermittent run-to-run controllers are designed to achieve the stability of singular discrete-time neural networks with state-dependent coefficients. The controllers are designed for two reasons: 1) it is very difficult and almost impossible to only measure the in situ feedback information for the controllers and 2) the controllers may not always exist at any time. The stability is then established for singular discrete-time neural networks with state-dependent coefficients. Finally, numerical simulations are shown to illustrate the usefulness of the obtained criteria.
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Saravanan S, Umesha V, Syed Ali M, Padmanabhan S. Exponential passivity for uncertain neural networks with time-varying delays based on weighted integral inequalities. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.07.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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20
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Yang Y, Liao X, Dong T. Period-adding bifurcation and chaos in a hybrid Hindmarsh–Rose model. Neural Netw 2018; 105:26-35. [DOI: 10.1016/j.neunet.2018.04.009] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2017] [Revised: 03/08/2018] [Accepted: 04/10/2018] [Indexed: 11/30/2022]
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21
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Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.04.026] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Wan P, Jian J. Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays. ISA TRANSACTIONS 2018; 74:88-98. [PMID: 29455890 DOI: 10.1016/j.isatra.2018.02.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 12/18/2017] [Accepted: 02/04/2018] [Indexed: 06/08/2023]
Abstract
This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results.
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Affiliation(s)
- Peng Wan
- College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
| | - Jigui Jian
- College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
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Wei H, Chen C, Tu Z, Li N. New results on passivity analysis of memristive neural networks with time-varying delays and reaction–diffusion term. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.10.035] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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25
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Sowmiya C, Raja R, Cao J, Rajchakit G, Alsaedi A. Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay. ADVANCES IN DIFFERENCE EQUATIONS 2017; 2017:318. [PMID: 29071005 PMCID: PMC5635139 DOI: 10.1186/s13662-017-1378-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 09/25/2017] [Indexed: 06/07/2023]
Abstract
This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.
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Affiliation(s)
- C Sowmiya
- Department of Mathematics, Alagappa University, Karaikudi, 630 004 India
| | - R Raja
- Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004 India
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing, 210096 China
| | - G Rajchakit
- Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand
| | - Ahmed Alsaedi
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
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Passivity Analysis of Stochastic Memristor-Based Complex-Valued Recurrent Neural Networks with Mixed Time-Varying Delays. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9687-2] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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27
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Liu J, Xu R. Delay-Dependent Passivity and Stability Analysis for a Class of Memristor-Based Neural Networks with Time Delay in the Leakage Term. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9594-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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28
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Wang G, Zang S, Wang X, Yuan F, Iu HHC. Memcapacitor model and its application in chaotic oscillator with memristor. CHAOS (WOODBURY, N.Y.) 2017; 27:013110. [PMID: 28147502 DOI: 10.1063/1.4973238] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
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Affiliation(s)
- Guangyi Wang
- Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Shouchi Zang
- Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Xiaoyuan Wang
- Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Fang Yuan
- Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Herbert Ho-Ching Iu
- School of Electrical, Electronic, and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
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Ren SY, Wu J, Wei PC. Passivity and Pinning Passivity of Coupled Delayed Reaction–Diffusion Neural Networks with Dirichlet Boundary Conditions. Neural Process Lett 2016. [DOI: 10.1007/s11063-016-9557-3] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Xiao J, Li Y, Zhong S, Xu F. Extended dissipative state estimation for memristive neural networks with time-varying delay. ISA TRANSACTIONS 2016; 64:113-128. [PMID: 27264155 DOI: 10.1016/j.isatra.2016.05.007] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Revised: 05/02/2016] [Accepted: 05/13/2016] [Indexed: 06/05/2023]
Abstract
This paper investigates the problem of extended dissipative state estimation for memristor-based neural networks (MNNs) with time-varying delay. Based on both nonsmooth analysis and the construction of a new Lyapunov-Krasovskii functional, the extended dissipative state estimation criteria are obtained by mainly applying differential inclusions, set-valued maps and many new integral inequalities. The extended dissipative state estimation can be adopted to deal with l2-l∞ state estimation, H∞ state estimation, passive state estimation and dissipative state estimation by valuing the corresponding weighting matrices. Finally, two numerical examples are given to show the effectiveness and less conservatism of the proposed criteria.
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Affiliation(s)
- Jianying Xiao
- School of Sciences, Southwest Petroleum University, Chengdu 610050, PR China; School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China.
| | - Yongtao Li
- College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610050, PR China
| | - Shouming Zhong
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China
| | - Fang Xu
- School of Sciences, Southwest Petroleum University, Chengdu 610050, PR China
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Relaxed exponential passivity criteria for memristor-based neural networks with leakage and time-varying delays. INT J MACH LEARN CYB 2016. [DOI: 10.1007/s13042-016-0565-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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32
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Radhika T, Nagamani G. Dissipativity analysis of stochastic memristor-based recurrent neural networks with discrete and distributed time-varying delays. NETWORK (BRISTOL, ENGLAND) 2016; 27:237-267. [PMID: 27385193 DOI: 10.1080/0954898x.2016.1196834] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, based on the knowledge of memristor-based recurrent neural networks (MRNNs), the model of the stochastic MRNNs with discrete and distributed delays is established. In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the MRNNs. In this model, the delay interval is decomposed into two subintervals by using the tuning parameter α such that 0 < α < 1. By constructing proper Lyapunov-Krasovskii functional and employing direct delay decomposition technique, several sufficient conditions are given to guarantee the dissipativity and passivity of the stochastic MRNNs with discrete and distributed delays in the sense of Filippov solutions. Using the stochastic analysis theory and Itô's formula for stochastic differential equations, we establish sufficient conditions for dissipativity criterion. The dissipativity and passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved by using Matlab Tools. Finally, three numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- Thirunavukkarasu Radhika
- a Department of Mathematics , Gandhigram Rural Institute - Deemed University , Gandhigram , Tamil Nadu , India
| | - Gnaneswaran Nagamani
- a Department of Mathematics , Gandhigram Rural Institute - Deemed University , Gandhigram , Tamil Nadu , India
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Thuan M, Trinh H, Hien L. New inequality-based approach to passivity analysis of neural networks with interval time-varying delay. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.02.051] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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34
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Li R, Cao J, Tu Z. Passivity analysis of memristive neural networks with probabilistic time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.01.035] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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35
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Anbuvithya R, Mathiyalagan K, Sakthivel R, Prakash P. Passivity of memristor-based BAM neural networks with different memductance and uncertain delays. Cogn Neurodyn 2016; 10:339-51. [PMID: 27468321 DOI: 10.1007/s11571-016-9385-1] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Accepted: 04/13/2016] [Indexed: 11/30/2022] Open
Abstract
This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov-Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.
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Affiliation(s)
- R Anbuvithya
- Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015 India
| | - K Mathiyalagan
- Department of Mathematics, Anna University-Regional Centre, Coimbatore, 641 047 India
| | - R Sakthivel
- Department of Mathematics, Sri Ramakrishna Institute of Technology, Coimbatore, 641 010 Tamil Nadu India ; Department of Mathematics, Sungkyunkwan University, Suwon, 440-746 The Republic of Korea
| | - P Prakash
- Department of Mathematics, Periyar University, Salem, 636 011 India
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36
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Mathiyalagan K, Park JH, Sakthivel R. Novel results on robust finite-time passivity for discrete-time delayed neural networks. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.10.125] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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37
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Meng Z, Xiang Z. Stability analysis of stochastic memristor-based recurrent neural networks with mixed time-varying delays. Neural Comput Appl 2016. [DOI: 10.1007/s00521-015-2146-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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38
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Xiao J, Zhong S, Li Y. Relaxed dissipativity criteria for memristive neural networks with leakage and time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.07.029] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Syed Ali M, Saravanakumar R, Cao J. New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.07.101] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Improved passivity criteria for memristive neural networks with interval multiple time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.07.075] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Xiao J, Zhong S, Li Y. New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays. ISA TRANSACTIONS 2015; 59:133-148. [PMID: 26434415 DOI: 10.1016/j.isatra.2015.09.008] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2015] [Revised: 08/30/2015] [Accepted: 09/07/2015] [Indexed: 06/05/2023]
Abstract
In this paper, the problem of passivity analysis is studied for memristor-based uncertain neural networks with leakage and time-varying delays. By combining differential inclusions with set-valued maps, the system of memristive neural networks is changed into the conventional one. By adding a triple quadratic integral and relaxing the requirement for the positive definiteness of some matrices, a proper Lyapunov-Krasovskii functional is constructed. Based on the establishment of the novel Lyapunov-Krasovskii functional, the new passivity criteria are derived by mainly applying Wirtinger-based double integral inequality, S-procedure and so on. Moreover, the conservatism of passivity conditions can be reduced. Finally, four numerical examples are given to show the effectiveness and less conservatism of the proposed criteria.
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Affiliation(s)
- Jianying Xiao
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China; School of Sciences, Southwest Petroleum University, Chengdu 610050, PR China.
| | - Shouming Zhong
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China
| | - Yongtao Li
- College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610050, PR China
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Li L, Jian J. Delay-dependent passivity analysis of impulsive neural networks with time-varying delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.05.098] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Meng Z, Xiang Z. Passivity analysis of memristor-based recurrent neural networks with mixed time-varying delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.03.016] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Global dissipativity of memristor-based complex-valued neural networks with time-varying delays. Neural Comput Appl 2015. [DOI: 10.1007/s00521-015-1883-2] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Wu A, Zeng Z. New global exponential stability results for a memristive neural system with time-varying delays. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2014.04.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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New results on passivity analysis of memristor-based neural networks with time-varying delays. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2014.05.032] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Zhao Z, Jian J. Attracting and quasi-invariant sets for BAM neural networks of neutral-type with time-varying and infinite distributed delays. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2014.03.015] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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