New results on robust stability for differential-difference systems with affine linear parametric uncertainty

Abstract

This article presents sufficient conditions to verify the robust stability property of convex combinations for quasipolynomials that 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.