Gyro motion boundedness under uncertain vehicle spin and acceleration

Using a quadratic Liapunov function, a condition is obtained for the boundedness of the motion of the gyro mounted in a vehicle which has a time-varying uncertain angular acceleration and deceleration omega-x(t) about the output axis, and is spinning with uncertain angular velocity omega-z(t) about the spin axis of the gyro. A region of ultimate boundedness in the theta-theta plane is obtained which the motion of the gyro eventually enters and in which it remains after a finite interval of time for any uncertain omega-x(t) and omega-z(t). The gyro motion is shown to be bounded if the uncertainty in the spin velocity does not exceed a certain threshold value. This condition disappears if omega-z(t) = 0.