Linear Stability Analysis of a Constant Quaternion Difference Attitude Controller

It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of general attitude trajectories. On account of this definitive result, and also because of the existence of powerful nonlinear control techniques, there has been relatively very little work analyzing the limits and performance of linear attitude control. It is the purpose of this paper to provide a characterization of the stability achievable for one class of linear attitude control problems, namely those leading to a constant quaternion difference. In this paper, we analytically derive a critical error angle below which linearized dynamics lead to natural marginal stability for such a system, and above which the system is unstable. The dynamics are then used to derive a locally stable linear attitude controller whose performance is validated using simulations.