Robust and Hölder-Continuous Finite-Time Stabilization of Rigid Body Attitude Dynamics Using Rotation Matrices

This article presents a robust and finite-time stable control scheme for attitude stabilization of a rigid body using a Hölder-continuous differentiator. This scheme is designed directly on the state-space of rigid body rotational motion, which is the tangent bundle of the Lie group of three-dimensional rotations. This article presents the differentiator, its stability and robustness properties in detail. This is followed by its use in the attitude stabilization control scheme. The stability and robustness properties of the proposed Hölder-continuous design are obtained through a Lyapunov stability analysis, and juxtaposed with a sliding-mode design. This is followed by numerical simulation results that compare the performance of the two designs. These comparison results clearly demonstrate the advantages of the proposed Holder-continuous stabilization scheme for rigid body attitude control.