Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

Xiaofei Fan; Xian Zhang; Ligang Wu; Michael Shi

doi:10.1109/TCBB.2016.2552519

Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

Xiaofei Fan
, Xian Zhang^*
, Ligang Wu
, Michael Shi

^*Corresponding author for this work

School of Astronautics

Heilongjiang University
Royal Melbourne Institute of Technology University

Research output: Contribution to journal › Article › peer-review

66 Scopus citations

Abstract

This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.

Original language	English
Article number	7450634
Pages (from-to)	868-879
Number of pages	12
Journal	IEEE/ACM Transactions on Computational Biology and Bioinformatics
Volume	14
Issue number	4
DOIs	https://doi.org/10.1109/TCBB.2016.2552519
State	Published - 1 Jul 2017

Keywords

Genetic regulatory networks (GRNs)
finite-time stability
reaction-diffusion terms
time-varying delays

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10.1109/TCBB.2016.2552519

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title = "Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays",

abstract = "This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.",

keywords = "Genetic regulatory networks (GRNs), finite-time stability, reaction-diffusion terms, time-varying delays",

author = "Xiaofei Fan and Xian Zhang and Ligang Wu and Michael Shi",

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T1 - Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

AU - Fan, Xiaofei

AU - Zhang, Xian

AU - Wu, Ligang

AU - Shi, Michael

PY - 2017/7/1

Y1 - 2017/7/1

N2 - This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.

AB - This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.

KW - Genetic regulatory networks (GRNs)

KW - finite-time stability

KW - reaction-diffusion terms

KW - time-varying delays

UR - https://www.scopus.com/pages/publications/85029544066

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DO - 10.1109/TCBB.2016.2552519

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JO - IEEE/ACM Transactions on Computational Biology and Bioinformatics

JF - IEEE/ACM Transactions on Computational Biology and Bioinformatics

IS - 4

M1 - 7450634

ER -

Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

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Keywords

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