## Abstract and Applied Analysis

### ${H}_{\infty }$ Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

#### Abstract

This paper is concerned with the ${H}_{\infty }$ filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to design ${H}_{\infty }$ 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 ${H}_{\infty }$ 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 ${H}_{\infty }$ disturbance attenuation level than one in (Liu et al., 2012).

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 257971, 12 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412605907

Digital Object Identifier
doi:10.1155/2014/257971

Mathematical Reviews number (MathSciNet)
MR3178859

Zentralblatt MATH identifier
07022016

#### Citation

Wang, Yantao; Zhou, Xingming; Zhang, Xian. ${H}_{\infty }$ Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 257971, 12 pages. doi:10.1155/2014/257971. https://projecteuclid.org/euclid.aaa/1412605907

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