Robust stability analysis of stochastic delayed genetic regulatory networks with polytopic uncertainties and linear fractional parametric uncertainties

•We have investigated the robust stability for delayed genetic regulatory networks with parameter uncertainties.•The parameter uncertainties are modeled as both polytopic form and structured linear fractional form.•We use different approaches for different types of integral term.•The rigorous constraint that the time-derivatives of time-varying delays must be less than one has been removed.

This study examines the problem of robust stability of uncertain stochastic genetic regulatory networks with time-varying delays. The system’s uncertainties are modeled as both polytopic form and structured linear fractional form. Based on a novel augmented Lyapunov–Krasovskii functional and different integral approaches, new stability conditions have been derived. Furthermore, these stability criteria can be applicable to both fast and slow time-varying delays. Finally, a numerical example is presented to illustrate the effectiveness of the proposed stability conditions.