On Global Asymptotic Stability and Stability of Saddle Solutions at Infinity

摘要

Methods of nonlinear analysis are widely used in control theory, optimization, and other areas; these methods have furnished significant results [1]-[4] in problems of oscillation theory, stability theory, and in problems involving oscillatory processes in automatic control systems. The theory of the stability of motion is concerned with the study of the action of perturbing factors on the motion of the system under consideration; besides, the perturbing forces are not taken into account in the equations of motion themselves, because they are small compared with the main forces. In the general case, these perturbing forces are unknown. If they act continuously, then the equations of motion under study differ from the true equations and they must be supplemented by correction terms.