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.

Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays

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
  • 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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