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Zhang X, Wang D, Ota K, Dong M, Li H. Delay-Dependent Switching Approaches for Stability Analysis of Two Additive Time-Varying Delay Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:7545-7558. [PMID: 34255633 DOI: 10.1109/tnnls.2021.3085555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
This article analyzes the exponentially stable problem of neural networks (NNs) with two additive time-varying delay components. Disparate from the previous solutions on this similar model, switching ideas, that divide the time-varying delay intervals and treat the small intervals as switching signals, are introduced to transfer the studied problem into a switching problem. Besides, delay-dependent switching adjustment indicators are proposed to construct a novel set of augmented multiple Lyapunov-Krasovskii functionals (LKFs) that not only satisfy the switching condition but also make the suitable delay-dependent integral items be in the each corresponding LKF based on each switching mode. Combined with some switching techniques, some less conservativeness stability criteria with different numbers of switching modes are obtained. In the end, two simulation examples are performed to demonstrate the effectiveness and efficiency of the presented methods comparing other available ones.
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Zhong X, Ren J, Gao Y. Passivity-based Bipartite Synchronization of Coupled Delayed Inertial Neural Networks via Non-reduced Order Method. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10839-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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3
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Liu F, Liu H, Liu K. New asymptotic stability analysis for generalized neural networks with additive time-varying delays and general activation function. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.08.066] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Li H, Li C, Ouyang D, Nguang SK, He Z. Observer-Based Dissipativity Control for T-S Fuzzy Neural Networks With Distributed Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:5248-5258. [PMID: 32191908 DOI: 10.1109/tcyb.2020.2977682] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
An observer-based dissipativity control for Takagi-Sugeno (T-S) fuzzy neural networks with distributed time-varying delays is studied in this article. First, the network channel delays are modeled as a distributed delay with its kernel. To make full use of kernels of the distributed delay, a Lyapunov-Krasovskii functional (LKF) is established with the kernel of the distributed delay. It is noted that the novel LKF and delay-dependent reciprocally convex inequality plays an important role in dealing with global asymptotical stability and strict (Q, S,R) - α -dissipativity of the T-S fuzzy delayed model. Through the constructed LKF, a new set of less conservative linear matrix inequality (LMI) conditions is presented to obtain an observer-based controller for the T-S fuzzy delayed model. This proposed observer-based controller ensures that the state of the closed-loop system is globally asymptotically stable and strictly (Q, S,R) - α -dissipative. Finally, the effectiveness of the proposed results is shown in numerical simulations.
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Zhang H, Qiu Z, Cao J, Abdel-Aty M, Xiong L. Event-Triggered Synchronization for Neutral-Type Semi-Markovian Neural Networks With Partial Mode-Dependent Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020; 31:4437-4450. [PMID: 31870995 DOI: 10.1109/tnnls.2019.2955287] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article studies the event-triggered stochastic synchronization problem for neutral-type semi-Markovian jump (SMJ) neural networks with partial mode-dependent additive time-varying delays (ATDs), where the SMJ parameters in two ATDs are considered to be not completely the same as the one in the connection weight matrices of the systems. Different from the weak infinitesimal operator of multi-Markov processes, a new one for the double semi-Markovian processes (SMPs) is first proposed. To reduce the conservative of the stability criteria, a generalized reciprocally convex combination inequality (RCCI) is established by the virtue of an interesting technique. Then, based on an eligible stochastic Lyapunov-Krasovski functional, three novel stability criteria for the studied systems are derived by employing the new RCCI and combining with a well-designed event-triggered control scheme. Finally, three numerical examples and one practical engineering example are presented to show the validity of our methods.
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Saravanakumar R, Mukaidani H, Muthukumar P. Extended dissipative state estimation of delayed stochastic neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.106] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Zhou J, Zhao T. State estimation for neural networks with two additive time-varying delay components using delay-product-type augmented Lyapunov–Krasovskii functionals. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.03.037] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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8
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Yuan Y, Song Q, Liu Y, Alsaadi FE. Synchronization of complex-valued neural networks with mixed two additive time-varying delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.12.023] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Zhang H, Qiu Z, Xiong L. Stochastic stability criterion of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.12.028] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Hua C, Wang Y, Wu S. Stability analysis of neural networks with time-varying delay using a new augmented Lyapunov–Krasovskii functional. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.08.044] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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11
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Qian W, Li Y, Chen Y, Yang Y. Delay-dependent L–L state estimation for neural networks with state and measurement time-varying delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.11.075] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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12
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Fractional delay segments method on time-delayed recurrent neural networks with impulsive and stochastic effects: An exponential stability approach. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.10.003] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Zhang XM, Han QL, Ge X, Ding D. An overview of recent developments in Lyapunov–Krasovskii functionals and stability criteria for recurrent neural networks with time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.06.038] [Citation(s) in RCA: 160] [Impact Index Per Article: 26.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Xiong JJ, Zhang G. Improved Stability Criterion for Recurrent Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:5756-5760. [PMID: 29994375 DOI: 10.1109/tnnls.2018.2795546] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this brief, the problem of delay-dependent stability of recurrent neural networks with time-varying delays is studied. A newly augmented Lyapunov-Krasovskii functional (LKF) that considers the information of the nonzero lower bound of time-varying delays is developed. Moreover, the information of the delayed state terms is not considered as elements of augmented vectors when constructing the LKF. An improved stability criterion with the framework of linear matrix inequalities is derived by employing the integral inequality and reciprocally convex combination. With the comparison to the existing ones, the developed stability criterion for neural networks has less conservatism and complexity. Finally, two widely used numerical examples are given to show the effectiveness and superiority of the obtained stability criterion.
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Lin WJ, He Y, Zhang CK, Long F, Wu M. Dissipativity analysis for neural networks with two-delay components using an extended reciprocally convex matrix inequality. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2018.03.021] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Samidurai R, Rajavel S, Cao J, Alsaedi A, Ahmad B. New Delay-Dependent Stability Criteria for Impulsive Neural Networks with Additive Time-Varying Delay Components and Leakage Term. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9855-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Improved results on sampled-data synchronization of Markovian coupled neural networks with mode delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.11.066] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Zhang G, Wang T, Li T, Fei S. Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.10.021] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Zhang XM, Han QL, Wang Z, Zhang BL. Neuronal State Estimation for Neural Networks With Two Additive Time-Varying Delay Components. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:3184-3194. [PMID: 28422702 DOI: 10.1109/tcyb.2017.2690676] [Citation(s) in RCA: 95] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper is concerned with the state estimation for neural networks with two additive time-varying delay components. Three cases of these two time-varying delays are fully considered: 1) both delays are differentiable uniformly bounded with delay-derivative bounded by some constants; 2) one delay is continuous uniformly bounded while the other is differentiable uniformly bounded with delay-derivative bounded by certain constants; and 3) both delays are continuous uniformly bounded. First, an extended reciprocally convex inequality is introduced to bound reciprocally convex combinations appearing in the derivative of some Lyapunov-Krasovskii functional. Second, sufficient conditions are derived based on the extended inequality for three cases of time-varying delays, respectively. Third, a linear-matrix-inequality-based approach with two tuning parameters is proposed to design desired Luenberger estimators such that the error system is globally asymptotically stable. This approach is then applied to state estimation on neural networks with a single interval time-varying delay. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.
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Dharani S, Rakkiyappan R, Cao J, Alsaedi A. Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach. Cogn Neurodyn 2017; 11:369-381. [PMID: 28761556 DOI: 10.1007/s11571-017-9438-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Revised: 03/21/2017] [Accepted: 04/10/2017] [Indexed: 11/29/2022] Open
Abstract
This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.
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Affiliation(s)
- S Dharani
- School of Mathematics, Bharathiar University, Coimbatore, Tamilnadu 641 046 India
| | - R Rakkiyappan
- School of Mathematics, Bharathiar University, Coimbatore, Tamilnadu 641 046 India
| | - Jinde Cao
- School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096 China.,Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
| | - Ahmed Alsaedi
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
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Song Q, Shu H, Zhao Z, Liu Y, Alsaadi FE. Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.015] [Citation(s) in RCA: 53] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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24
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Ding L, He Y, Liao Y, Wu M. New result for generalized neural networks with additive time-varying delays using free-matrix-based integral inequality method. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.01.056] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Chen H, Zhang Z, Wang H. Robust H∞ state-feedback control for linear systems. Proc Math Phys Eng Sci 2017; 473:20160934. [PMID: 28484336 PMCID: PMC5415696 DOI: 10.1098/rspa.2016.0934] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Accepted: 03/14/2017] [Indexed: 11/12/2022] Open
Abstract
This paper investigates the problem of robust H∞ control for linear systems. First, the state-feedback closed-loop control algorithm is designed. Second, by employing the geometric progression theory, a modified augmented Lyapunov-Krasovskii functional (LKF) with the geometric integral interval is established. Then, parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill. This technique can eliminate the unnecessary enlargement of the LKF derivative estimation, which gives less conservatism. In addition, the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed H∞ performance in the presence of a disturbance input and parameter uncertainties. A liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example. It shows that this proposed state-feedback control approach achieves the expected results for linear systems in the sense of the prescribed H∞ performance.
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Affiliation(s)
- Hao Chen
- College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, People’s Republic of China
- Research Centre for Applied Science, Computing and Engineering, Glyndwr University, Wrexham LL11 2AW, UK
| | - Zhenzhen Zhang
- College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, People’s Republic of China
| | - Huazhang Wang
- College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, People’s Republic of China
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Manivannan R, Samidurai R, Cao J, Alsaedi A, Alsaadi FE. Global exponential stability and dissipativity of generalized neural networks with time-varying delay signals. Neural Netw 2017; 87:149-159. [DOI: 10.1016/j.neunet.2016.12.005] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2016] [Revised: 11/05/2016] [Accepted: 12/13/2016] [Indexed: 11/26/2022]
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27
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Yang J, Luo WP, Chen H, Liu XL. Dual delay-partitioning approach to stability analysis of generalized neural networks with interval time-varying delay. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.07.027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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28
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Muthukumar P, Subramanian K. Stability criteria for Markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.03.058] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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29
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Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw 2016; 81:1-10. [DOI: 10.1016/j.neunet.2016.04.012] [Citation(s) in RCA: 140] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2016] [Revised: 04/25/2016] [Accepted: 04/29/2016] [Indexed: 11/22/2022]
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30
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Bao G, Zeng Z. Global asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functions. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.02.017] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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