Stability considerations in quaternion attitude control using discontinuous Lyapunov functions

Unit quaternions are a powerful tool for singularity free analysis and the control of arbitrary amplitude motion in a three-dimensional space. The authors present the use of proportional derivative quaternion feedback stabilisation for relative motion attitude control. Global asymptotic stability is guaranteed by defining a particular Lyapunov function and formal requirements are established. Conditions for a finite time control are also presented.