Robust stability for genetic regulatory networks with linear fractional uncertainties

In this paper, the asymptotic stability analysis problem for a class of delayed genetic regulatory networks (GRNs) with linear fractional uncertainties and stochastic perturbations is studied. By employing a more effective Lyapunov functional and using a lemma to estimate the derivative of the Lyapunov functional, some new sufficient conditions for the stability problem of GRNs are derived in terms of linear matrix inequality (LMI). Finally, two numerical examples are used to demonstrate the usefulness of the main results and less conservatism of the derived conditions.

► A new Lyapunov–Krasovskii functional includes four adjusting terms which may reduce conservative is proposed.
► Both the differentiable and non-differentiable time-varying delays are considered.
► This paper has taken the linear fractional uncertainties into account, which is more general than the other two uncertainty type.
► A lemma is used to avoiding overly bounding of the integral terms.