Stability analysis of delayed GRNs

Xian Zhang; Yantao Wang; Ligang Wu

doi:10.1007/978-3-030-17098-1_3

Stability analysis of delayed GRNs

Xian Zhang^*
, Yantao Wang
, Ligang Wu

^*Corresponding author for this work

Heilongjiang University
School of Astronautics, Harbin Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

10 Scopus citations

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].

Original language	English
Title of host publication	Studies in Systems, Decision and Control
Publisher	Springer International Publishing
Pages	57-80
Number of pages	24
DOIs	https://doi.org/10.1007/978-3-030-17098-1_3
State	Published - 2019
Externally published	Yes

Publication series

Name	Studies in Systems, Decision and Control
Volume	207
ISSN (Print)	2198-4182
ISSN (Electronic)	2198-4190

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10.1007/978-3-030-17098-1_3

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author = "Xian Zhang and Yantao Wang and Ligang Wu",

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AU - Zhang, Xian

AU - Wang, Yantao

AU - Wu, Ligang

PY - 2019

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N2 - 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].

AB - 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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Stability analysis of delayed GRNs

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