Robust Hurwitz stability test for linear systems with uncertain commensurate time delays

The note deals with the robust Hurwitz stability of a class of linear systems with uncertain commensurate time delays, which is formulated as the robust Hurwitz stability of a nonpolytopic family of quasi-polynomials, a NP-hard problem from the viewpoint of computational complexity. On the basis of the "edge theorem" and Sylvester resultant elimination, a necessary and sufficient condition is developed for the robust stability of the whole family, and it yields an effective testing procedure. An illustrative example is given to show the effectiveness of the method.