Asymptotic and robust stability of genetic regulatory networks with time-varying delays

The robust asymptotic stability problem of genetic regulatory networks with time-varying delays is investigated. Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into two subintervals, and then the convexity property of the matrix inequality and the free weighting matrix method are fully used in this paper. By using a Lyapunov functional approach and linear matrix inequality techniques, the stability criteria for the delayed genetic regulatory networks are expressed as a set of linear matrix inequalities (LMIs), which can lead to much less conservative analysis results. A genetic network example is given to illustrate that the results in this paper are more effective and less conservative than some existing ones.