On roughness conditions for unstable nonautonomous linear systems in terms of stability type preservation

The paper discusses the conditions under which the instability of equilibrium condition of nonautonomous linear systems of any order grades into instability of equilibrium condition of corresponding nonlinear perturbed systems under certain class nonlinear perturbations of their right-hand members (unstable nonautonomous linear system roughness in terms of stability type preservation). Sufficient conditions of such roughness are formulated for certain classes of nonlinear perturbations).