New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

We propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative suff...

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Main Authors: Yanfeng Zhao, Jihong Shen, Dongyan Chen
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2016/7634680
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spelling doaj-fb982a99bdb549ce99616ce83862825b2020-11-25T01:41:18ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/76346807634680New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic DisturbancesYanfeng Zhao0Jihong Shen1Dongyan Chen2College of Automation, Harbin Engineering University, Harbin 150001, ChinaCollege of Science, Harbin Engineering University, Harbin 150001, ChinaDepartment of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaWe propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative sufficient condition is obtained in terms of linear matrix inequalities (LMIs) by using the combination of the lower bound lemma, the discrete-time Jensen inequality, and the free-weighting matrix method. It is shown that the proposed results can be readily solved by using the Matlab software. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the theoretical results.http://dx.doi.org/10.1155/2016/7634680
collection DOAJ
language English
format Article
sources DOAJ
author Yanfeng Zhao
Jihong Shen
Dongyan Chen
spellingShingle Yanfeng Zhao
Jihong Shen
Dongyan Chen
New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
Mathematical Problems in Engineering
author_facet Yanfeng Zhao
Jihong Shen
Dongyan Chen
author_sort Yanfeng Zhao
title New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
title_short New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
title_full New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
title_fullStr New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
title_full_unstemmed New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
title_sort new stability criterion for discrete-time genetic regulatory networks with time-varying delays and stochastic disturbances
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2016-01-01
description We propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative sufficient condition is obtained in terms of linear matrix inequalities (LMIs) by using the combination of the lower bound lemma, the discrete-time Jensen inequality, and the free-weighting matrix method. It is shown that the proposed results can be readily solved by using the Matlab software. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the theoretical results.
url http://dx.doi.org/10.1155/2016/7634680
work_keys_str_mv AT yanfengzhao newstabilitycriterionfordiscretetimegeneticregulatorynetworkswithtimevaryingdelaysandstochasticdisturbances
AT jihongshen newstabilitycriterionfordiscretetimegeneticregulatorynetworkswithtimevaryingdelaysandstochasticdisturbances
AT dongyanchen newstabilitycriterionfordiscretetimegeneticregulatorynetworkswithtimevaryingdelaysandstochasticdisturbances
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