This paper is devoted to the study of the problem of exponential asymptotic
stability of the rotational motion of a gyrostat using servo-control momen
ts which are applied to the internal rotors. The servo-control moments whic
h impose the rotational motion are obtained. The stabilizing servo-control
moments are obtained from the conditions to ensure exponential asymptotic s
tability of the desired motion. Estimations of the phase coordinates as exp
onential functions are presented. The method based on a choice of the struc
tural form of the servo-control moments such that the equations of motion r
educe to a system of differential equations with exponential asymptotic sta
bility of an special solution.