Exponential control of a rotational motion of a rigid body using quaternions

摘要

A new developed technique is used to study the problem of the exponential stabilization of the rotational motion of a rigid body about a fixed axis in the body with the help of rotors. In this technique, the exponential asymptotic stability of this motion is proved. The control moments leading to the rotational motion are obtained. The conditions that ensure the exponential asymptotic stabilization of this motion are used to obtain the stabilizing control law as non-linear functions of the phase coordinates of the system. Finally, many special cases and analyzing the results of the studied problem are investigated.