New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays

• Published in: Neurocomputing (Amsterdam) Vol. 207; pp. 763 - 771
• Main Authors: Li, Zhen, Chen, Dongyan, Liu, Yurong, Zhao, Yanfeng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 26.09.2016
• Subjects: Convex combination approach; Free-weighting matrix method; GRNs; Jensen inequality; Time-varying delays; GRNs; Time-varying delays; Convex combination approach; Free-weighting matrix method; Jensen inequality
• ISSN: 0925-2312; 1872-8286
• DOI: 10.1016/j.neucom.2016.05.066

In this paper, the stability analysis problem is investigated for a class of genetic regulatory networks (GRNs) with time-varying delays. Here, the addressed GRNs are modelled by the nonlinear differential equations. A new Lyapunov–Krasovkii functional is constructed by additionally introducing some triple integral terms. By employing the Jensen inequality, the free-weighting matrix and the convex combination idea, a semi-definite programme approach is developed to derive new sufficient condition guaranteeing the global asymptotic stability of the addressed GRNs subject to time-varying delays. Subsequently, a new stability criterion is proposed for GRNs with time-varying delays when the upper bounds of the derivative of the time delays are unknown. It is shown that the feasibility of presented results can be readily checked by using the standard numerical software. Finally, we provide two numerical examples to illustrate the effectiveness and less conservativeness of the proposed stability criteria. •A delay-dependent stability criterion is proposed for GRNs with time-varying delays.•A new Lyapunov–Krasovkii functional is constructed by additionally introducing some triple integral terms.•New results with less conservatism are given based on the Jensen inequality, the free-weighting matrix and the convex combination idea.