Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term

Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term

This paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs) with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information...

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Main Authors: Jun Li, Manfeng Hu, Jinde Cao, Yongqing Yang, Yinghua Jin
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/706720
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spelling doaj-23269b45292c4f9cb4868da2cb9fbd222020-11-24T20:55:22ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/706720706720Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage TermJun Li0Manfeng Hu1Jinde Cao2Yongqing Yang3Yinghua Jin4School of Science, Jiangnan University, Wuxi 214122, ChinaSchool of Science, Jiangnan University, Wuxi 214122, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaSchool of Science, Jiangnan University, Wuxi 214122, ChinaSchool of Science, Jiangnan University, Wuxi 214122, ChinaThis paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs) with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information on the lower bound of the delay sufficiently, a delay-dependent stability criterion is derived for the proposed UISGRNs model by using the free-weighting matrices method and convex combination technique. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. In addition, three numerical examples are given to justify the obtained stability results.http://dx.doi.org/10.1155/2014/706720
collection DOAJ
language English
format Article
sources DOAJ
author Jun Li
Manfeng Hu
Jinde Cao
Yongqing Yang
Yinghua Jin
spellingShingle Jun Li
Manfeng Hu
Jinde Cao
Yongqing Yang
Yinghua Jin
Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term
Abstract and Applied Analysis
author_facet Jun Li
Manfeng Hu
Jinde Cao
Yongqing Yang
Yinghua Jin
author_sort Jun Li
title Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term
title_short Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term
title_full Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term
title_fullStr Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term
title_full_unstemmed Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term
title_sort stability of uncertain impulsive stochastic genetic regulatory networks with time-varying delay in the leakage term
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description This paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs) with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information on the lower bound of the delay sufficiently, a delay-dependent stability criterion is derived for the proposed UISGRNs model by using the free-weighting matrices method and convex combination technique. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. In addition, three numerical examples are given to justify the obtained stability results.
url http://dx.doi.org/10.1155/2014/706720
work_keys_str_mv AT junli stabilityofuncertainimpulsivestochasticgeneticregulatorynetworkswithtimevaryingdelayintheleakageterm
AT manfenghu stabilityofuncertainimpulsivestochasticgeneticregulatorynetworkswithtimevaryingdelayintheleakageterm
AT jindecao stabilityofuncertainimpulsivestochasticgeneticregulatorynetworkswithtimevaryingdelayintheleakageterm
AT yongqingyang stabilityofuncertainimpulsivestochasticgeneticregulatorynetworkswithtimevaryingdelayintheleakageterm
AT yinghuajin stabilityofuncertainimpulsivestochasticgeneticregulatorynetworkswithtimevaryingdelayintheleakageterm
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