Root Distribution Criteria for Some Polynomial Families and Their Applications

抄録

The present paper is concerned with the conditions under which for a familiy of polynomials, every member has a given number of roots in the open left-half plane and the other roots in the open right-half plane. Simple criteria for such root distribution invariance are provided for some families of polynomials, including the interval and diamond polynomial families. Using one of them, some extreme point results are presented for the Hurwitz stability of the weighted diamond family.