Sector Bound-Dependent Matrix-Separation-Based Inequality and its Application to Stability Analysis of Discrete-Time Delayed Genetic Regulatory Networks

In this brief, a class of sector bound-dependent matrix-separation-based inequality is proposed that can utilize the properties of nonlinear functions to overcome the weaknesses of existing estimation methods. Then, an expanded class of Lyapunov–Krasovskii functional is constructed to include some integral terms of the sector constraint of nonlinear functions. By applying the improved inequality, the stability criterion of genetic regulatory networks (GRNs) with stochastic perturbations and time-varying delay is established. The validity of presented criterion and the advancement of proposed method are analysed based on two examples.