Sets of stability of multiparameter problems

We consider a linear ODE's system with constant coefficients depending on several parameters. The set of stability of the system is the set of those values of parameters, for which the stationary point of the system is stable. We show that the boundary of the set of stability can be computed by means of the elimination theory and the Hurvitz rule, which are described in textbooks on algebra. We consider separately general (non-Hamiltonian) systems (§2) and Hamiltonian systems (§3). Examples of such computations are given.