Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Li, Fu-Dong, Zhu, Qi, Xu, Hao-Tian and Jiang, Lin ORCID: 0000-0001-6531-2791 (2017) Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality MATHEMATICAL PROBLEMS IN ENGINEERING, 2017 (1). pp. 1-16. ISSN 1024-123X, 1563-5147

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Abstract

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature.

Item Type:	Article
Uncontrolled Keywords:	40 Engineering, 10 Reduced Inequalities
Depositing User:	Symplectic Admin
Date Deposited:	05 Dec 2017 10:47
Last Modified:	22 May 2026 18:22
DOI:	10.1155/2017/4157256
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3013559
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