Geometry of the multidimensional stability domain in the space of even (odd) coefficients of the characteristic polynomial of linear systems

The necessary and sufficient conditions for asymptotic stability of the linear systems based on separate analysis of the spaces of even and odd coefficients of the characteristic polynomial were proposed. Consideration was given to the characteristic polynomials with positive and negative coefficients in the highest term. The stability domain in the space of even (odd) coefficients was proved to obey a system of linear inequalities and represent a convex polyhedral cone with vertex at the origin. Some properties of the convex polyhedral cones were analyzed. The problem of intersection of an arbitrary number of stability domains was solved, in particular, and examples were presented.