An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays.

Abstract

This paper focuses on stability analysis for a class of genetic regulatory networks with interval time-varying delays. An improved integral inequality concerning on double-integral items is first established. Then, we use the improved integral inequality to deal with the resultant double-integral items in the derivative of the involved Lyapunov-Krasovskii functional. As a result, a delay-range-dependent and delay-rate-dependent asymptotical stability criterion is established for genetic regulatory networks with differential time-varying delays. Furthermore, it is theoretically proven that the stability criterion proposed here is less conservative than the corresponding one in [Neurocomputing, 2012, 93: 19-26]. Based on the obtained result, another stability criterion is given under the case that the information of the derivatives of delays is unknown. Finally, the effectiveness of the approach proposed in this paper is illustrated by a pair of numerical examples which give the comparisons of stability criteria proposed in this paper and some literature.