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

Abstract

In this paper, the robust stability problem is investigated for a class of delayed genetic regulatory networks (GRNs) with uncertain parameters. Here, the uncertain parameters are modeled as having a structured linear fractional parameteric uncertainties form. By choosing an appropriate Lyapunov-Krasovkii functional and combining the Jensen inequality method with the free-weighting matrix method, some sufficient conditions are proposed to guarantee the asymptotical stability of the addressed systems. Subsequently, the stability criteria are presented for the GRNs in the linear matrix inequalities (LMIs), which can be easily tested by using the standard numerical software. Finally, a numerical example is employed to show the effectiveness of the proposed stability criteria.