Delayed Feedback Asymptotic Stabilization of Rigid Body Attitude Motion for Large Rotations∗

The delayed feedback control of rigid body attitude motion is addressed where there is an unknown time delay in the feedback measurement. The attitude motion is described on the tangent bundle TSO(3) to globally and uniquely represent the orientation of the rigid body, while a continuous nonlinear delayed feedback control law is proposed for local asymptotic stabilization on TSO(3). For this purpose, we introduce a notion based on the Lyapunov technique, which combines the Morse-Lyapunov method with Lyapunov-Krasovskii technique to yield a suitable Morse-Lyapunov-Krasovskii (M-L–K) functional, from which the stability conditions and proper control gain matrices are obtained in terms of linear matrix inequalities (LMIs). Simulations illustrate the performance of the proposed control scheme.