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Stability Analysis of Delayed GRNs

  • Xian ZhangEmail author
  • Yantao Wang
  • Ligang Wu
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 207)

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical ScienceHeilongjiang UniversityHarbinChina
  2. 2.School of AstronauticsHarbin Institute of TechnologyHarbinChina

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