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.