Robust stability analysis of delayed Takagi–Sugeno fuzzy genetic regulatory networks

Abstract

In this paper, the nonlinear model of genetic regulatory networks is described by the Takagi–Sugeno fuzzy model representation with time-varying delays. Due to the highly complicated nonlinear stability and robust stability problems, a fuzzy approximation method is employed to interpolate several linear genetic regulatory networks at different operation points via fuzzy bases to approximate the nonlinear genetic regulatory network. In this context, the methods of the linear matrix inequality (LMI) technique could be employed to simplify the problems related to robust stability of genetic regulatory networks. Further, by involving triple integral terms in Lyapunov–Krasovskii functionals and LMI techniques, the stability criteria for the delayed fuzzy genetic regulatory networks are expressed as a convex combination of LMIs, which can be solved numerically by any LMI solvers. Several numerical examples are given to verify the effectiveness and applicability of the derived approach.