Time dependence of the attainability regions of third order systems

A linear steady third order system with one controlling (perturbing) action that is bounded in absolute magnitude is considered. The matrix specifying the system has one real and two complex conjugate eigenvalues. The behaviour of the boundary of the attainability region of this system as time increases is studied. It is shown that the structure of the boundary of the attainability region depends on the relation between the real eigenvalue and the real part of the complex conjugate eigenvalues.