Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

S. Lakshmanan; Fathalla A. Rihan; R. Rakkiyappan; Ju H. Park

doi:10.1016/j.nahs.2014.04.003

Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

S. Lakshmanan, Fathalla A. Rihan, R. Rakkiyappan, Ju H. Park

Department of Mathematical Sciences

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

60 Citations (Scopus)

Abstract

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov-Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Nonlinear Analysis: Hybrid Systems
Volume	14
DOIs	https://doi.org/10.1016/j.nahs.2014.04.003
Publication status	Published - Nov 2014

Keywords

Genetic regulatory networks
Linear matrix inequalities
Markovian jumping parameters
Stability
Time-delay

ASJC Scopus subject areas

Control and Systems Engineering
Analysis
Computer Science Applications

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10.1016/j.nahs.2014.04.003

Cite this

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abstract = "In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov-Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.",

keywords = "Genetic regulatory networks, Linear matrix inequalities, Markovian jumping parameters, Stability, Time-delay",

author = "S. Lakshmanan and Rihan, {Fathalla A.} and R. Rakkiyappan and Park, {Ju H.}",

note = "Funding Information: This work was supported by UAE University ( UAEU-NRF-7-20886 ). The work of J.H. Park was supported by NRF of Korea ( 2013R1A1A2A10005201 ). The authors would like to thank the referees for their valuable comments which improved the manuscript. ",

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AU - Lakshmanan, S.

AU - Rihan, Fathalla A.

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AU - Park, Ju H.

N1 - Funding Information: This work was supported by UAE University ( UAEU-NRF-7-20886 ). The work of J.H. Park was supported by NRF of Korea ( 2013R1A1A2A10005201 ). The authors would like to thank the referees for their valuable comments which improved the manuscript.

PY - 2014/11

Y1 - 2014/11

N2 - In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov-Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.

AB - In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov-Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.

KW - Genetic regulatory networks

KW - Linear matrix inequalities

KW - Markovian jumping parameters

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KW - Time-delay

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Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

Abstract

Keywords

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