Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms
This study seeks to address the finite-time robust stability of delayed genetic regulatory networks (GRNs) with uncertain parameters and reaction-diffusion terms. We employ an appropriate Lyapunov-Krasovskii functional to derive some less conservative stability criteria for GRNs under Dirichlet boun...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/8565437 |
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| _version_ | 1832548566364585984 |
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| author | Wenqin Wang Yali Dong Shouming Zhong Feng Liu |
| author_facet | Wenqin Wang Yali Dong Shouming Zhong Feng Liu |
| author_sort | Wenqin Wang |
| collection | DOAJ |
| description | This study seeks to address the finite-time robust stability of delayed genetic regulatory networks (GRNs) with uncertain parameters and reaction-diffusion terms. We employ an appropriate Lyapunov-Krasovskii functional to derive some less conservative stability criteria for GRNs under Dirichlet boundary conditions, which are delay-dependent, delay-derivative-dependent, and reaction-diffusion-dependent. The time-varying delays and their derivatives are both bounded with lower and upper bounds, where the lower bound of them can be zero or non-zero. In addition, we define some new variables to deal with uncertain parameters. Moreover, Jensen’s integral inequality, Wirtinger-type integral inequality, reciprocally convex combination inequality, Gronwall inequality, and Green formula are employed to handle integral terms. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the obtained stability criteria. |
| format | Article |
| id | doaj-art-b985a9c809924931bb2e1387e730a331 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b985a9c809924931bb2e1387e730a3312025-02-03T06:13:47ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/85654378565437Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion TermsWenqin Wang0Yali Dong1Shouming Zhong2Feng Liu3School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaDepartment of Radiology and Tianjin Key Laboratory of Functional Imaging, Tianjin Medical University General Hospital, Tianjin 300052, ChinaThis study seeks to address the finite-time robust stability of delayed genetic regulatory networks (GRNs) with uncertain parameters and reaction-diffusion terms. We employ an appropriate Lyapunov-Krasovskii functional to derive some less conservative stability criteria for GRNs under Dirichlet boundary conditions, which are delay-dependent, delay-derivative-dependent, and reaction-diffusion-dependent. The time-varying delays and their derivatives are both bounded with lower and upper bounds, where the lower bound of them can be zero or non-zero. In addition, we define some new variables to deal with uncertain parameters. Moreover, Jensen’s integral inequality, Wirtinger-type integral inequality, reciprocally convex combination inequality, Gronwall inequality, and Green formula are employed to handle integral terms. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the obtained stability criteria.http://dx.doi.org/10.1155/2019/8565437 |
| spellingShingle | Wenqin Wang Yali Dong Shouming Zhong Feng Liu Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms Complexity |
| title | Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_full | Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_fullStr | Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_full_unstemmed | Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_short | Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_sort | finite time robust stability of uncertain genetic regulatory networks with time varying delays and reaction diffusion terms |
| url | http://dx.doi.org/10.1155/2019/8565437 |
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