ON THE STABILITY OF STEADY MOTIONS OF SYSTEMS WITH CYCLIC COORDINATES

A method of solving stabilization problems by isolating a controlled subsystem of possibly smaller dimension [1, 2] is developed further. The stabilizing action is determined by the solution of an optimal stabilization problem [3] for a linear controlled subsystem. The control that is found is implemented in the form of a feedback loop that uses an estimate [4] of the state vector (or part of it) constructed by measuring the perturbations of the positional coordinates. The stability of the unperturbed motion in a complete closed system is established by reducing the problem to a special case of the theory of critical cases [5, 6] or to the problem of stability under constantly acting perturbations [6].