Gyro Motion Boundedness under Uncertain Angular Acceleration about Vehicle Output Axis

An analysis of the motion of a single-axis rate gyroscope mounted in a space vehicle which has uncertain time-varying acceleration and deceleration ωx(t) about the output axis of the gyro is presented. Using a Lyapunov function, a condition for boundedness of the gyro motion is derived. It is shown that by a proper selection of the parameters of the gyro, its motion can be forced to remain in a small neighborhood (called region of ultimate boundedness) of the origin in θ - θ plane after a certain finite interval of time for any bounded uncertain ωx(t). Analytical relations for the selection of gyro parameters to keep the error caused in the measurement of the input rate due to ωx within desirable limits are derived.