The Lyapunov stability analysis on restraint loops of a two-degree-of-freedom gyro

Abstract

The stability of the restraint loops of a two degree-of-freedom (DOF) gyro has been analyzed by means of the Lyapunov direct method. The state-space model is derived from the technical functions of a 2-DOF gyro, which is a fourth-order system and time varying during the starting process. From the variable gradient method, the Lyapunov function is found, and whereby the stability conditions of the system are obtained. Since the starting process of a gyro is much longer than the time constant of the restraint loops for time-varying systems, it can be stabilized as long as the stability conditions are changed along with the time varying parameters.