Abstract
This chapter is concerned with the problem of \(H_\infty \) state estimation for a class of discrete-time GRNs with random delay and external disturbance. The random delay is described by a Markovian chain. The aim is to estimate the concentrations of mRNAs and proteins by designing \(H_\infty \) filter based on available measurement outputs. By using the LKF method, a sufficient LMI condition is first established to ensure the filtering error system to be stochastically stable with a prescribed \(H_\infty \) disturbance attenuation level. The condition is dependent on the transition probability matrix of the random delay. Then, the filter gains are represented via a feasible solution of the LMIs. Moreover, an optimization problem with LMIs constraints is established to design an \(H_\infty \) filter which ensures an optimal \(H_\infty \) disturbance attenuation level. The effectiveness of the proposed approach is illustrated by a numerical example.
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Zhang, X., Wang, Y., Wu, L. (2019). \(H_{\infty }\) State Estimation for Delayed Discrete-Time GRNs. In: Analysis and Design of Delayed Genetic Regulatory Networks. Studies in Systems, Decision and Control, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-030-17098-1_11
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DOI: https://doi.org/10.1007/978-3-030-17098-1_11
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