Finite-gain L∞ stabilization of satellite formation flying with input saturation

In this paper, we consider a formation keeping problem for a satellite formation flying system. The relative motion dynamics is designed with polytopic uncertainties by considering elliptical reference orbit, noncoplarnar formation and unknown angular rate, angular acceleration within some boundary. We propose a composite nonlinear feedback control law obtained by the solution to an algebraic Riccati inequality (ARI). Then, in the presence of input saturation and disturbances, internal and external stability (Finite-gain L_∞ stability) of the relative motion dynamics are investigated using proposed control law. Finally, numerical examples is presented to demonstrate the validity of the proposed controller.