Parameter-Dependent Lyapunov Function Method Applied to Satellite Formation Keeping Control

In this paper, a parameter-dependent Lyapunov function method is applied to design robust controller for a satellite formation flying system around the Earth based on an uncertainty model derived from a nonlinear relative position equation. In this model, nonzero eccentricity and varying semi-major axis are included as parametric uncertainties. Exogenous perturbations including J2 perturbation, atmospheric drag and actuation are bounded by functional uncertainties. The model can be regarded as a polytopic type uncertain system with 8 vertices, then the parameter-dependent Lyapunov function is proposed to design H-2 and H-infinity controllers respectively to maintain the relative position of the formation flying system. The simulation demonstrates that the proposed controller can realize the control the satellites formation-keeping.