Stability Analysis of Fuzzy Genetic Regulatory Networks with Various Time Delays
Document Type
Article
Publication Date
1-1-2018
Abstract
The synthetic genetic regulatory networks (GRNs) prove to be a powerful tool in studying gene regulation processes in living organisms. In order to take vagueness into consideration, fuzzy theory is incorporated in the GRNs and we found a novel system, namely fuzzy genetic regulatory networks (FGRNs). By applying the Homeomorphism theorem, we demonstrated an existence, uniqueness, and asymptotic stability analysis of the equilibrium point of FGRNs with time delay in the leakage term and unbounded distributed delays. By utilizing Lyapunov functional method and the linear matrix inequality (LMI) techniques, some new and useful criteria of the FGRNs with respect to the equilibrium point are derived. The derived criteria are of the form of LMI, and hence they can be verified easily. Finally, illustrative example with simulations are demonstrated to prove the effectiveness of the proposed results.
Keywords
Asymptotic stability, Fuzzy genetic regulatory networks, Homeomorphism theorem, Leakage delay, Linear matrix inequality
Divisions
MathematicalSciences
Funders
University of Malaya HIR Grant UM.C/625/1/HIR/ MOHE/SC/13
Publication Title
Bulletin of the Malaysian Mathematical Sciences Society
Volume
41
Issue
1
Publisher
Springer Verlag