An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays
It will be settled out for the open problem of designing an r-order finite-time (F-T) state observer for reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays. By assuming the Dirichlet boundary conditions, aiming to estimate the mRNA and protein concentrations via availab...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/7257083 |
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| _version_ | 1849412957074620416 |
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| author | Xiaofei Fan Yantao Wang Ligang Wu Xian Zhang |
| author_facet | Xiaofei Fan Yantao Wang Ligang Wu Xian Zhang |
| author_sort | Xiaofei Fan |
| collection | DOAJ |
| description | It will be settled out for the open problem of designing an r-order finite-time (F-T) state observer for reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays. By assuming the Dirichlet boundary conditions, aiming to estimate the mRNA and protein concentrations via available network measurements. Firstly, sufficient F-T stability conditions for the filtering error system have been investigated via constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using several integral inequalities and (reciprocally) convex technique simultaneously. These conditions are delay-dependent and reaction-diffusion-dependent and can be checked by MATLAB toolbox. Furthermore, a method is proposed to design an r-order F-T state observer, and the explicit expressions of observer gains are given. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-662fa16fcc704cfdb6fbb9a91ba72d5c |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-662fa16fcc704cfdb6fbb9a91ba72d5c2025-08-20T03:34:17ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/72570837257083An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying DelaysXiaofei Fan0Yantao Wang1Ligang Wu2Xian Zhang3School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSpace Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaIt will be settled out for the open problem of designing an r-order finite-time (F-T) state observer for reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays. By assuming the Dirichlet boundary conditions, aiming to estimate the mRNA and protein concentrations via available network measurements. Firstly, sufficient F-T stability conditions for the filtering error system have been investigated via constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using several integral inequalities and (reciprocally) convex technique simultaneously. These conditions are delay-dependent and reaction-diffusion-dependent and can be checked by MATLAB toolbox. Furthermore, a method is proposed to design an r-order F-T state observer, and the explicit expressions of observer gains are given. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2018/7257083 |
| spellingShingle | Xiaofei Fan Yantao Wang Ligang Wu Xian Zhang An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays Complexity |
| title | An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays |
| title_full | An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays |
| title_fullStr | An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays |
| title_full_unstemmed | An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays |
| title_short | An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays |
| title_sort | r order finite time state observer for reaction diffusion genetic regulatory networks with time varying delays |
| url | http://dx.doi.org/10.1155/2018/7257083 |
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