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2019 | OriginalPaper | Chapter

3. Stability Analysis of Delayed GRNs

Authors : Xian Zhang, Yantao Wang, Ligang Wu

Published in: Analysis and Design of Delayed Genetic Regulatory Networks

Publisher: Springer International Publishing

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Abstract

The chapter first proves an inequality concerning with double integrals by partitioning the integral domain into two parts and exchanging the order of double integrals over a sub-domain. Then it is mathematically proven that the proposed integral inequality is less conservative than Lemma 1.​14(ii). Thereby, for a class of GRNs with time-varying delays, a pair of delay-range-dependent and delay-rate-dependent asymptotic stability criteria are investigated by constructing an appropriate LKF and applying reciprocally convex techniques. The obtained stability criteria are given in the form of LMIs, which can be easily checked by the Toolbox YALMIP of MATLAB. Furthermore, it is theoretically proven that a stability criterion proposed in this chapter is less conservative than [25, Corollary 3.1]. Finally, numerical examples and their simulation results show that the stability criteria proposed in this chapter may be less conservative than ones in [13, 21, 25, 28, 30]

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previous chapter Stability Analysis for GRNs with Mixed Delays
next chapter Stability Analysis for Delayed Switching GRNs
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Metadata
Title
Stability Analysis of Delayed GRNs
Authors
Xian Zhang
Yantao Wang
Ligang Wu
Copyright Year
2019
Book
Analysis and Design of Delayed Genetic Regulatory Networks

Print ISBN: 978-3-030-17097-4

Electronic ISBN: 978-3-030-17098-1

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-17098-1_3

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