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\(H_{\infty }\) State Estimation for Delayed Discrete-Time GRNs

  • Xian ZhangEmail author
  • Yantao Wang
  • Ligang Wu
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 207)

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical ScienceHeilongjiang UniversityHarbinChina
  2. 2.School of AstronauticsHarbin Institute of TechnologyHarbinChina

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