Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Abstract

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of LyapunovKrasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range-and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature.

Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

“…In the cell cycle, delays are shown to affect the cell cycle [ 31 ] by inducing cell arrest and apoptosis through the p53 network upon sensing damaged DNA [ 32 ]. These and many other existing works, such as [ 33 , 34 , 35 ] to mention a few, have analysed delayed systems deterministically. However, there are increasing attempts to study the behaviour of stochastic systems with the time delay [ 36 , 37 , 38 ].…”