Abstract: A new approach to stabilization of tethered satellites during station keeping is presented. It is observed that results from the critical stabilization must be applied in the construction of the stabilizing law for a tethered satellite system when the tether is assumed rigid and massless. Our method is the combination of the centre manifold theory and Lyapunov method. When compared with Liaw and Abed's method, in which tools related to the Hopf bifurcation are employed, it avoids calculating the Floquet exponents and is easily mastered by control engineers.

Key words: tethered satellite system, critical stabilization, Lyapunov method, centre manifold theory