Robust delay-probability-distribution-dependent stability of uncertain genetic regulatory networks with time-varying delays

• We have investigated the robust delay-probability-distribution-dependent stability for delayed genetic regulatory networks with parameter uncertainties.
• The parameter uncertainties are modeled as having a structured linear fractional form.
• An augmented novel Lyapunov–Krasovskii functional which contains some triple integral terms has been chosen.
• We divide the time-varying delays into multiple nonuniformly subinterval and use the lower bound lemma together with the Jensen inequality lemma.
• The rigorous constraint that the time-derivatives of time-varying delays must be less than one has been removed.

This study is concerned with the problem of robust delay-probability-distribution-dependent stability of genetic regulatory networks with time-varying delays and parameter uncertainties. By dividing the time-varying delays into multiple nonuniformly subinterval and choosing an appropriate novel Lyapunov functional which contains some triple integral terms, new stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs). The uncertain parameters are modeled as having a structured linear fractional form. Besides, the derivatives of the time delays are considered having different bounds in various delay intervals. Moreover, less conservative conditions are obtained by using the lower bound lemma together with Jensen inequality lemma. Furthermore, the criteria can be applicable to both fast and slow time-varying delays. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.