Analysis of stability for the controlled spacecraft with a deployable and retractable flexible appendage

In this paper we analyse the stability of the controlled spacecraft with a deployable and retractable flexible appendage. The center body of the spacecraft is controlled by PD controller. According to Lyapunov stable theory and unstable theory, we firstly give the new stability criterion about finite time and then deduce the sufficient conditions which will guarantee the closed-loop system stable or will cause the system unstable during retracting the appendage. At last we verify the existence of these sufficient conditions by simulations and the results of simulations are coherent to the theoretic results given by the new stability criterion. The research of this paper is instructive for designing the control law and the proper rate of deployment and retraction of the appendage to guarantee the system asymptotic stable.