Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays

LIU Jinliang; YUE Dong

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Article Navigation > Chinese Journal of Electronics > 2013 > 22(2): 263-268

LIU Jinliang and YUE Dong, “Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 263-268, 2013,

Citation:

LIU Jinliang and YUE Dong, “Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 263-268, 2013,

LIU Jinliang and YUE Dong, “Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 263-268, 2013,

Citation:

LIU Jinliang and YUE Dong, “Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays,” Chinese Journal of Electronics, vol. 22, no. 2, pp. 263-268, 2013,

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Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays

LIU Jinliang¹,
YUE Dong²

1.
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, China;
2.
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Funds: This work is partly supported by the National Natural Science Foundation of China (No.61074025, No.61074024, No.60834002, No.60904013), the Natural Science Foundation of Jiangsu Province of China (No.BK2012469, No.BK2012847), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Received Date: 2011-12-01
Rev Recd Date: 2012-07-01
Publish Date: 2013-04-25

Abstract

Abstract

This paper investigates the asymptotic stability of genetic regulatory networks with random delays and Markovian jumping parameters. The delay considered here is assumed to be satisfying a certain stochastic characteristic. Corresponding to the probability of the delay taking value in different intervals, stochastic variables satisfying Bernoulli random binary distribution are introduced and a new system model is established by employing the information of the probability distribution. By using a Lyapunov functional approach and linear matrix inequality techniques, the stability criteria for the delayed Markovian jumping genetic regulatory networks are expressed as a set of Linear matrix inequalities (LMIs), which can be solved numerically by LMI toolbox in MATLAB. A genetic network example is given to verify the effectiveness and the applicability of the proposed approach.
- Genetic regulatory network,
- Random delays,
- Asymptotic stability,
- Markovian jumping parameters

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References(17)

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