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LIU Jinliang, YUE Dong. Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays[J]. Chinese Journal of Electronics, 2013, 22(2): 263-268.
Citation: LIU Jinliang, YUE Dong. Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays[J]. Chinese Journal of Electronics, 2013, 22(2): 263-268.
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Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays

  • 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.
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  • Received Date: November 30, 2011
  • Revised Date: June 30, 2012
  • Published Date: April 24, 2013
    Graphical 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.
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    • References (17)
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