Abstract
Problems in the construction of equations of perturbed motions for state and semi-state systems are discussed. It is shown that in most cases it is not possible to construct the equations of the perturbed motions, so that the classical approach to the stability analysis of a selected motion is not applicable. The necessary and sufficient stability conditions that provide the testing of stability of an arbitrary system motion, without the utilization of the equations of perturbed motions, are developed. The results obtained concern the original Lyapunov stability definition and contain as special cases some other existing stability results. Two examples are worked out: one of them concerns the analysis of a non-linear feedback system that does not possess a state model.