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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)

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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

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