本文首先注意到滞后型拟多项式与中立型拟多项式零点分布的根本区别，并指出一些通常的事实：如特征根对时滞的连续依赖性，所有特征根位于开左半复平面与稳定性的等价关系等对于中立型系统都不成立，然后建立了中立型拟多项式胞鲁棒稳定性的边界定理．依此将可公度时滞中立型系统族的鲁棒稳定性化为相应拟多项式胞所有边的Ｈｕｒｗｉｔｚ稳定性与其中立型项构成的子胞所有边的Ｓｃｈｕｒ稳定性的判定．最后给出了检验中立型胞鲁棒稳定性的一个有效的图解法．

This paper firstly notices a fundamental difference of the distribution of zeros between retarded quasi-polynomials and neutral quasi-polynomials.It is shown that some common facts,such as the continuous dependence on time delays for eigenvalues,the equiyaleat relation between the stability and all eigenvalues within the strict left-half complex plane and so on do not carry over to neutral systems.Then,the Edge Theorem is developed for robust stability analysis of a polytope of neutral quasi-polynomials.Based on the Edge Theorem,the robust stability of a family of neutral systems with commensurate delays is reduced to the checking of the H(Hurwitz)-stability of all the edges of a polytope of quasi-polynomials and the Schur stability of all the edges of the subpolytope of neutral terms. Finally,an effective graphical test is made for checking the robust stability of a polytope of neutral quasi-polynomials.