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H∞ Filtering for Discrete‐Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

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Listed:
  • Yantao Wang
  • Xingming Zhou
  • Xian Zhang

Abstract

This paper is concerned with the H∞ filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to design H∞ filter to estimate the true concentrations of mRNAs and proteins based on available measurement data. By introducing an appropriate Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs) which makes the filtering error system stochastically stable with a prescribed H∞ disturbance attenuation level. The filter gains are given by solving the LMIs. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach; that is, our approach is available for a smaller H∞ disturbance attenuation level than one in (Liu et al., 2012).

Suggested Citation

  • Yantao Wang & Xingming Zhou & Xian Zhang, 2014. "H∞ Filtering for Discrete‐Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:257971
    DOI: 10.1155/2014/257971
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    References listed on IDEAS

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    1. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
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