A less conservative stability criterion for delayed stochastic genetic regulatory networks (Q1719108)

Summary: This paper concerns the problem of stability analysis for delayed stochastic genetic regulatory networks. By introducing an appropriate Lyapunov-Krasovskii functional and employing delay-range partition approach, a new stability criterion is given to ensure the mean square stability of genetic regulatory networks with time-varying delays and stochastic disturbances. The stability criterion is given in the form of linear matrix inequalities, which can be easily tested by the LMI Toolbox of MATLAB. Moreover, it is theoretically shown that the obtained stability criterion is less conservative than the one in [\textit{W. Zhang} et al., Commun. Nonlinear Sci. Numer. Simul. 17, No. 4, 1753--1765 (2012; Zbl 1239.92041)]. Finally, a numerical example is presented to illustrate our theory.