The problem of Routh–Hurwitz stability of a polynomial matrix family is considered as that of discovering the structure of the stability domain in the parameter space. Algorithms for finding the spectral abscissa and the distance to instability from any internal point of the stability domain to its boundary for the case of real perturbations are proposed. The treatment is performed in the ideology of analytical algorithm for elimination of variables and localization of zeros of algebraic systems. Some examples are given.