Robust stability analysis for a class of linear time-delay systems

This paper presents sufficient conditions to verify the robust stability property of convex combinations for quasipolynomials which they represent the characteristic equation of differential-difference dynamics systems. It considers affine linear parametric uncertainty structure in the coefficients of quasipolynomials and also, interval uncertainty in the time delay. First of all, a transformation of the delay's operator is performed in order to get a two variable polynomial; after this, to obtain the robust stability property, a result based on the Hurwitz matrix is applied.