Abstract: The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality

Key words: stability, nonautonomous system, frequently-acting perturbation, state transition matrix, robot