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

Xue Zhang; Yu Xue; Xue Zhang; Yu Xue

doi:10.3934/math.2024185

AIMS Mathematics

2024, Volume 9, Issue 2: 3763-3787. doi: 10.3934/math.2024185

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Research article

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

Xue Zhang ^1,2,
Yu Xue ^{1,2
,
,}

1.
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, China

Received: 22 October 2023 Revised: 20 December 2023 Accepted: 31 December 2023 Published: 10 January 2024
MSC : 93B53

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.
- genetic regulatory networks,
- time-varying delays,
- $ H_{\infty} $ state observer design,
- bounded real lemma,
- parameterized bounds of solutions
Citation: Xue Zhang, Yu Xue. A novel $ H_{\infty} $ state observer design method for genetic regulatory networks with time-varying delays[J]. AIMS Mathematics, 2024, 9(2): 3763-3787. doi: 10.3934/math.2024185

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Abstract

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.

References

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