Existence of real roots for the family of interval polynomials

In this paper, existences of real roots for the family of interval polynomials with one or two variables are discussed. We proved that for the family of interval polynomials with one variable, it has no real root if and only if four vertex point polynomials have no real root, and for the case of two variables, we just need to test whether eight polynomials have real root. This method will simplify the computations greatly. At last, we will apply the results of this paper to the problem of robust stability of the time delay systems.