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Wang J, Ji Z, Zhang H, Wang Z, Meng Q. Synchronization of Generally Uncertain Markovian Inertial Neural Networks With Random Connection Weight Strengths and Image Encryption Application. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:5911-5925. [PMID: 34910641 DOI: 10.1109/tnnls.2021.3131512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
This article focuses on the synchronization problem of delayed inertial neural networks (INNs) with generally uncertain Markovian jumping and their applications in image encryption. The random connection weight strengths and generally uncertain Markovian are discussed in the INNs model. Compared with most existing INNs models that have constant connection weight strengths, our model is more practical because connection weight strengths of INNs may randomly vary due to the external and internal environment and human factor. The delay-range-dependent synchronization conditions (DRDSCs) could be obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, two examples are shown to demonstrate the effectiveness of the proposed results.
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2
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$$H_\infty $$ State Estimation for Round-Robin Protocol-Based Markovian Jumping Neural Networks with Mixed Time Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10598-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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3
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Wang J, Wang Z, Chen X, Qiu J. Synchronization criteria of delayed inertial neural networks with generally Markovian jumping. Neural Netw 2021; 139:64-76. [PMID: 33684610 DOI: 10.1016/j.neunet.2021.02.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Revised: 12/27/2020] [Accepted: 02/04/2021] [Indexed: 10/22/2022]
Abstract
In this paper, the synchronization problem of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. The second order differential equations are transformed into the first-order differential equations by utilizing the variable transformation method. The Markovian process in the systems is uncertain or partially known due to the delay of data transmission channel or the loss of data information, which is more general and practicable to consider generally Markovian jumping inertial neural networks. The synchronization criteria can be obtained by using the delay-dependent Lyapunov-Krasovskii functionals and higher order polynomial based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, the numerical examples are provided to demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- Junyi Wang
- Faculty of Robot Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China; School of Automation and Electrical Engineering, Linyi University, Linyi, Shandong, 276005, China.
| | - Zhanshan Wang
- College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China.
| | - Xiangyong Chen
- School of Automation and Electrical Engineering, Linyi University, Linyi, Shandong, 276005, China; Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong, Linyi University, Linyi, Shandong, 276005, China.
| | - Jianlong Qiu
- School of Automation and Electrical Engineering, Linyi University, Linyi, Shandong, 276005, China; Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong, Linyi University, Linyi, Shandong, 276005, China.
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Yang H, Wang Z, Shen Y, Alsaadi FE, Alsaadi FE. Event-triggered state estimation for Markovian jumping neural networks: On mode-dependent delays and uncertain transition probabilities. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.10.050] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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5
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Zhang P, Hu J, Zhang H, Chen D. H ∞ sliding mode control for Markovian jump systems with randomly occurring uncertainties and repeated scalar nonlinearities via delay-fractioning method. ISA TRANSACTIONS 2020; 101:10-22. [PMID: 32008731 DOI: 10.1016/j.isatra.2020.01.032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2018] [Revised: 01/20/2020] [Accepted: 01/23/2020] [Indexed: 06/10/2023]
Abstract
This paper addresses the problem of robust H∞ sliding mode control (SMC) for discrete delayed Markovian jumping systems subject to randomly occurring uncertainties (ROUs) and repeated scalar nonlinearities (RSNs). Here, a set of mutually independent Bernoulli distributed random variables is introduced to model the phenomenon of the ROUs, where the occurrence probabilities could be uncertain. The purpose of paper is to present an H∞ SMC strategy via the delay-fractioning approach such that, for the Markovian jumping parameters, time-varying delays, ROUs and RSNs, the mean-square stability of the resulted sliding motion with a prescribed H∞ performance can be guaranteed. Subsequently, the robust sliding mode controller is synthesized to guarantee that the reachability condition in the discrete-time setting is ensured. Finally, the validity of proposed robust SMC strategy is verified by providing a simulation example.
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Affiliation(s)
- Panpan Zhang
- Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China; Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin 150080, China
| | - Jun Hu
- Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China; Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin 150080, China; School of Engineering, University of South Wales, Pontypridd CF37 1DL, UK.
| | - Hongxu Zhang
- School of Measurement and Communication, Harbin University of Science and Technology, Harbin 150080, China
| | - Dongyan Chen
- Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China; Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin 150080, China
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Chen W, Ding D, Mao J, Liu H, Hou N. Dynamical performance analysis of communication-embedded neural networks: A survey. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.08.088] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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7
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Memory-based State Estimation of T–S Fuzzy Markov Jump Delayed Neural Networks with Reaction–Diffusion Terms. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10026-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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8
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Li X, Li F, Zhang X, Yang C, Gui W. Exponential Stability Analysis for Delayed Semi-Markovian Recurrent Neural Networks: A Homogeneous Polynomial Approach. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:6374-6384. [PMID: 29994551 DOI: 10.1109/tnnls.2018.2830789] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper investigates the exponential stability analysis issue for a class of delayed recurrent neural networks (RNNs) with semi-Markovian parameters. By constructing a stochastic Lyapunov functional and using some zoom techniques to estimate its weak infinitesimal operator, the exponential mean square stability criteria have been proposed for the Markovian neural networks with certain transition probabilities. We then generalize the homogeneous polynomial approach for the delayed Markovian RNNs with uncertain transition probabilities during the stability analysis. Theoretical results have obtained by introducing an appropriate technique for dealing with a large number of complex homogeneous polynomial matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed technique.
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9
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Finite-time boundedness and stabilization of uncertain switched delayed neural networks of neutral type. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.07.020] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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10
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Zhang X, Wang H, Tian Y, Peyrodie L, Wang X. Model-free based neural network control with time-delay estimation for lower extremity exoskeleton. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.06.055] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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11
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Song Y, Hu J, Chen D, Liu Y, Alsaadi FE, Sun G. A resilience approach to state estimation for discrete neural networks subject to multiple missing measurements and mixed time-delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.06.065] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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12
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Choi HD, Ahn CK, Karimi HR, Lim MT. Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\infty }$ Performances. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:3195-3207. [PMID: 28166518 DOI: 10.1109/tcyb.2017.2655725] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper studies delay-dependent exponential dissipative and l2 - l∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l2 - l∞ senses. The design of the desired exponential dissipative and l2 - l∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.
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Li Y, Deng F, Li G, Jiao L. Robust
$$H_\infty$$
H
∞
filtering for uncertain discrete-time stochastic neural networks with Markovian jump and mixed time-delays. INT J MACH LEARN CYB 2017. [DOI: 10.1007/s13042-017-0651-2] [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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14
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Dong J, Fu Y. A design method for T–S fuzzy systems with partly immeasurable premise variables subject to actuator saturation. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.11.025] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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15
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Zha L, Fang JA, Liu J, Tian E. Event-based finite-time state estimation for Markovian jump systems with quantizations and randomly occurring nonlinear perturbations. ISA TRANSACTIONS 2017; 66:77-85. [PMID: 27876278 DOI: 10.1016/j.isatra.2016.11.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2016] [Revised: 10/26/2016] [Accepted: 11/11/2016] [Indexed: 06/06/2023]
Abstract
This paper is concerned with finite-time state estimation for Markovian jump systems with quantizations and randomly occurring nonlinearities under event-triggered scheme. The event triggered scheme and the quantization effects are used to reduce the data transmission and ease the network bandwidth burden. The randomly occurring nonlinearities are taken into account, which are governed by a Bernoulli distributed stochastic sequence. Based on stochastic analysis and linear matrix inequality techniques, sufficient conditions of stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are firstly derived for the existence of the desired estimator. Then, the explicit expression of the gain of the desired estimator are developed in terms of a set of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the usefulness of the theoretical results.
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Affiliation(s)
- Lijuan Zha
- College of Information Science and Technology, Donghua University, Shanghai, PR China
| | - Jian-An Fang
- College of Information Science and Technology, Donghua University, Shanghai, PR China.
| | - Jinliang Liu
- College of Information Engenering, Nanjing University of Finance and Economics, Nanjing, Jiangsu, PR China
| | - Engang Tian
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing,Jiangsu, PR China
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16
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A new approach to non-fragile state estimation for continuous neural networks with time-delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.02.062] [Citation(s) in RCA: 80] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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17
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Nagamani G, Ramasamy S, Meyer-Baese A. Robust dissipativity and passivity based state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays. Neural Comput Appl 2015. [DOI: 10.1007/s00521-015-2100-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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18
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Wei Y, Peng X, Qiu J, Jia S. H∞ filtering for two-dimensional continuous-time Markovian jump systems with deficient transition descriptions. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.04.054] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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19
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Fuzzy adaptive output feedback DSC design for SISO nonlinear stochastic systems with unknown control directions and dead-zones. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.04.078] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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20
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Stability in distribution of stochastic delay recurrent neural networks with Markovian switching. Neural Comput Appl 2015. [DOI: 10.1007/s00521-015-2013-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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21
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$$H_{\infty }$$ H ∞ Estimation for Markovian Jump Neural Networks With Quantization, Transmission Delay and Packet Dropout. Neural Process Lett 2015. [DOI: 10.1007/s11063-015-9460-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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22
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Zhong Q, Cheng J, Zhao Y. Delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays. ISA TRANSACTIONS 2015; 57:43-50. [PMID: 25683106 DOI: 10.1016/j.isatra.2015.01.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2014] [Revised: 10/25/2014] [Accepted: 01/04/2015] [Indexed: 06/04/2023]
Abstract
In this paper, a novel method is developed for delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays. New sufficient condition for stochastic boundness of Markovian jumping neural networks is presented and proved by an newly augmented stochastic Lyapunov-Krasovskii functional and novel activation function conditions, the state trajectory remains in a bounded region of the state space over a given finite-time interval. Finally, a numerical example is given to illustrate the efficiency and less conservative of the proposed method.
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Affiliation(s)
- Qishui Zhong
- School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
| | - Jun Cheng
- School of Electrical and Information Technology, Yunnan Minzu University, Kunming, Yunnan 650500, PR China.
| | - Yuqing Zhao
- Faculty of Mechanical and Electrical Engineering, Yunnan Agricultural University, Kunming, Yunnan 650201, PR China.
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Hua M, Tan H, Fei J. State estimation for uncertain discrete-time stochastic neural networks with Markovian jump parameters and time-varying delays. INT J MACH LEARN CYB 2015. [DOI: 10.1007/s13042-015-0373-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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24
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Mathiyalagan K, Su H, Shi P, Sakthivel R. Exponential H∞ filtering for discrete-time switched neural networks with random delays. IEEE TRANSACTIONS ON CYBERNETICS 2015; 45:676-687. [PMID: 25020225 DOI: 10.1109/tcyb.2014.2332356] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.
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25
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Shao L, Huang H, Zhao H, Huang T. Filter design of delayed static neural networks with Markovian jumping parameters. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.11.045] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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26
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Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2013.12.054] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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27
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Arunkumar A, Sakthivel R, Mathiyalagan K, Park JH. Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks. ISA TRANSACTIONS 2014; 53:1006-1014. [PMID: 24933353 DOI: 10.1016/j.isatra.2014.05.002] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2013] [Revised: 03/09/2014] [Accepted: 05/06/2014] [Indexed: 06/03/2023]
Abstract
This paper focuses the issue of robust stochastic stability for a class of uncertain fuzzy Markovian jumping discrete-time neural networks (FMJDNNs) with various activation functions and mixed time delay. By employing the Lyapunov technique and linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions are established for the robust stochastic stability of uncertain FMJDNNs. More precisely, the parameter uncertainties are assumed to be time varying, unknown and norm bounded. The obtained stability conditions are established in terms of LMIs, which can be easily checked by using the efficient MATLAB-LMI toolbox. Finally, numerical examples with simulation result are provided to illustrate the effectiveness and less conservativeness of the obtained results.
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Affiliation(s)
- A Arunkumar
- Department of Mathematics, Anna University-Regional Centre, Coimbatore 641047, India
| | - R Sakthivel
- Department of Mathematics, Sri Ramakrishna Institute of Technology, Coimbatore 641010, India; Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea.
| | - K Mathiyalagan
- Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan 712-749, Republic of Korea
| | - Ju H Park
- Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan 712-749, Republic of Korea
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29
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Cheng J, Zhu H, Zhong S, Zeng Y, Dong X. Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. ISA TRANSACTIONS 2013; 52:768-774. [PMID: 23958490 DOI: 10.1016/j.isatra.2013.07.015] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2012] [Revised: 06/20/2013] [Accepted: 07/27/2013] [Indexed: 06/02/2023]
Abstract
This paper is concerned with the problem of finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed. Based on the derived condition, the reliable H∞ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.
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Affiliation(s)
- Jun Cheng
- School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
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30
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Lee TH, Park JH, Kwon O, Lee S. Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 2013; 46:99-108. [DOI: 10.1016/j.neunet.2013.05.001] [Citation(s) in RCA: 148] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2012] [Revised: 01/29/2013] [Accepted: 05/02/2013] [Indexed: 11/25/2022]
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31
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A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Netw 2013; 46:50-61. [DOI: 10.1016/j.neunet.2013.04.014] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2013] [Revised: 04/25/2013] [Accepted: 04/28/2013] [Indexed: 11/23/2022]
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32
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pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching. Neural Process Lett 2013. [DOI: 10.1007/s11063-013-9297-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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33
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34
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State Estimation for Discrete-Time Neural Networks with Markov-Mode-Dependent Lower and Upper Bounds on the Distributed Delays. Neural Process Lett 2012. [DOI: 10.1007/s11063-012-9219-z] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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35
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Chen Y, Zheng WX. Stochastic state estimation for neural networks with distributed delays and Markovian jump. Neural Netw 2012; 25:14-20. [DOI: 10.1016/j.neunet.2011.08.002] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2010] [Revised: 06/17/2011] [Accepted: 08/06/2011] [Indexed: 10/17/2022]
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36
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Stability analysis for discrete delayed Markovian jumping neural networks with partly unknown transition probabilities. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.06.029] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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37
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Zhao Y, Zhang L, Shen S, Gao H. Robust stability criterion for discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions. ACTA ACUST UNITED AC 2010; 22:164-70. [PMID: 21134815 DOI: 10.1109/tnn.2010.2093151] [Citation(s) in RCA: 71] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
This brief is concerned with the robust stability problem for a class of discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions. The parameter uncertainties are considered to be norm-bounded, and the stochastic perturbations are described in terms of Brownian motion. Defective statistics means that the transition probabilities of the multimode neural networks are not exactly known, as assumed usually. The scenario is more practical, and such defective transition probabilities comprise three types: known, uncertain, and unknown. By invoking the property of the transition probability matrix and the convexity of uncertain domains, a sufficient stability criterion for the underlying system is derived. Furthermore, a monotonicity is observed concerning the maximum value of a given scalar, which bounds the stochastic perturbation that the system can tolerate as the level of the defectiveness varies. Numerical examples are given to verify the effectiveness of the developed results.
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Affiliation(s)
- Ye Zhao
- Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150080, China.
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