A reduction principle for asymptotically triangular differential systems

Problems of the stability of non-linear non-autonomous systems of differential equations with a special class of asymptotically vanishing perturbations are considered. The problem of reducing a problem on the stability of the equilibrium of a perturbed system to a problem on stability with respect to a non-linear approximation system which has a triangular form is solved. Applications of the results of the investigations to mechanical systems with a variable mass and time-varying equations of the constraints are presented.