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Global Exponential Stability Analysis of Discrete‐Time Genetic Regulatory Networks with Time Delays
Author(s) -
Li Yanjiang,
Zhang Xian,
Tan Chong
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.751
Subject(s) - invertible matrix , discrete time and continuous time , control theory (sociology) , mathematics , linear matrix inequality , exponential stability , stability (learning theory) , matrix (chemical analysis) , set (abstract data type) , exponential growth , constant (computer programming) , lti system theory , exponential function , invariant (physics) , mathematical optimization , computer science , linear system , control (management) , nonlinear system , mathematical analysis , physics , statistics , materials science , quantum mechanics , artificial intelligence , machine learning , pure mathematics , composite material , mathematical physics , programming language
This paper focuses on the study of global robust exponential stability of discrete‐time genetic regulatory networks ( GRNs ) with time‐invariant/time‐varying delays and parameter uncertainties. Many existing results on this problem are based on the linear matrix inequality ( LMI ) approach, which needs to verify whether there exists a feasible solution of a set of LMIs . Along with the increase in the number of genes, dimensions of LMIs will increase accordingly, which will lead to a large amount of calculation. Based on M ‐matrix theory, sufficient conditions ensuring the global robust exponential stability of a class of discrete‐time GRNs with time‐invariant/time‐varying delays and parameter uncertainties are presented. These given conditions are to check whether a constructed constant matrix is a nonsingular M‐matrix. Simulation results of several examples are given to demonstrate the validity of the proposed method.