Abstract
The problem of stabilizing motion in controlled systems with a guaranteed estimate of the control quality is considered. It arises from the optimal stabilization problem when the conditions on the cost functional are relaxed: no minimization of this functional is required, it is only necessary for it not to exceed a certain limit. This enables the class of solvable problems to be extended compared to the class of optimal stabilization problems. The solution of the problem is based on Lyapunov's direct method using Lyapunov functions with derivatives of constant sign. Some of the results are new even in the case of the optimal stabilization problem. The following examples are considered: a holonomic mechanical system with time-dependent Lagrangian, a controlled linear mechanical system and the problem of using the gravitational moment to stabilize the controlled plane rotational motion of a satellite in an elliptic orbit.
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