Abstract
The problem of finite‐time stability of switched genetic regulatory networks (GRNs) with time‐varying delays via Wirtinger’s integral inequality is addressed in this study. A novel Lyapunov–Krasovskii functional is proposed to capture the dynamical characteristic of GRNs. Using Wirtinger’s integral inequality, reciprocally convex combination technique and the average dwell time method conditions in the form of linear matrix inequalities (LMIs) are established for finite‐time stability of switched GRNs. The applicability of the developed finite‐time stability conditions is validated by numerical results.
Highlights
In recent years, genetic regulatory networks (GRNs) have received much research attention, and many interesting results have been reported [1,2,3,4,5,6,7,8]
Whereas in the differential equation model, the variables describe the concentrations of gene products, such as mRNA and proteins as continuous values of the gene regulation system, and this model talks about the concentrations of gene products such as mRNA and proteins as variables in
Since the biological system especially GRNs is a slow process of transcription, translation, and translocation [19,20,21,22,23], the time delay cannot be avoided
Summary
GRNs have received much research attention, and many interesting results have been reported [1,2,3,4,5,6,7,8]. In the Boolean model, the state converges to a terminal state via a series of state transitions that is determined by the Boolean rules In this model, the activity of each gene is expressed in one of two states, ON or OFF, which is determined by a Boolean function by its own and by other related states. Ere are many research results on the stability analysis for GRNs with time delay (e.g., [15,16,17,18]). It is of great importance to deal delayed GRNs. For instance, in [27], authors presented a different equation model for GRNs with constant time delays and proposed stability analysis for GRNs with time delays. In [28], authors developed delay dependent criteria for stability of GRNs with delay and freeweighting matrices
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