A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays

In this article, a novel method is proposed to investigate the $ H_{\infty} $ state observer design problem for genetic regulatory networks with time-varying delays and disturbances. First, the structure of the desired state observer is constructed, and the parameterized bounds of the error system s...

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Main Authors: Xue Zhang, Yu Xue
Format: Article
Language:English
Published: AIMS Press 2024-01-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2024185?viewType=HTML
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author Xue Zhang
Yu Xue
author_facet Xue Zhang
Yu Xue
author_sort Xue Zhang
collection DOAJ
description In this article, a novel method is proposed to investigate the $ H_{\infty} $ state observer design problem for genetic regulatory networks with time-varying delays and disturbances. First, the structure of the desired state observer is constructed, and the parameterized bounds of the error system solutions are given. Then, a bounded real lemma is established to provide the existence of the state observer and ensure that the error system is globally exponentially stable at an $ H_{\infty} $ performance level. Third, based on the obtained bounded real lemma, the explicit expressions of the $ H_{\infty} $ state observer can be obtained by solving several matrix inequalities. The effectiveness of the proposed novel observer design method is illustrated via a numerical example.
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spelling doaj.art-4c34db48514149179a411e21293761592024-01-29T01:31:05ZengAIMS PressAIMS Mathematics2473-69882024-01-01923763378710.3934/math.2024185A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delaysXue Zhang 0 Yu Xue 11. School of Mathematical Science, Heilongjiang University, Harbin 150080, China 2. Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin 150080, China1. School of Mathematical Science, Heilongjiang University, Harbin 150080, China 2. Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin 150080, ChinaIn this article, a novel method is proposed to investigate the $ H_{\infty} $ state observer design problem for genetic regulatory networks with time-varying delays and disturbances. First, the structure of the desired state observer is constructed, and the parameterized bounds of the error system solutions are given. Then, a bounded real lemma is established to provide the existence of the state observer and ensure that the error system is globally exponentially stable at an $ H_{\infty} $ performance level. Third, based on the obtained bounded real lemma, the explicit expressions of the $ H_{\infty} $ state observer can be obtained by solving several matrix inequalities. The effectiveness of the proposed novel observer design method is illustrated via a numerical example.https://www.aimspress.com/article/doi/10.3934/math.2024185?viewType=HTMLgenetic regulatory networkstime-varying delays$ h_{\infty} $ state observer designbounded real lemmaparameterized bounds of solutions
spellingShingle Xue Zhang
Yu Xue
A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays
AIMS Mathematics
genetic regulatory networks
time-varying delays
$ h_{\infty} $ state observer design
bounded real lemma
parameterized bounds of solutions
title A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays
title_full A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays
title_fullStr A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays
title_full_unstemmed A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays
title_short A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays
title_sort novel h infty state observer design method for genetic regulatory networks with time varying delays
topic genetic regulatory networks
time-varying delays
$ h_{\infty} $ state observer design
bounded real lemma
parameterized bounds of solutions
url https://www.aimspress.com/article/doi/10.3934/math.2024185?viewType=HTML
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