Hybrid feedback for global asymptotic stabilization on a compact manifold

In this paper, we employ a hybrid feedback control strategy to globally asymptotically stabilize a setpoint on a smooth compact manifold without boundary satisfying the following: there exists a finite maximal atlas such that the desired setpoint belongs to each chart of the atlas. The proposed hybrid controller includes a proportional-derivative (PD) action during flows and, at jumps, uses hysteresis to switch between local coordinate charts to stabilize the desired setpoint robustly with respect to exogenous disturbances. We show that the proposed controller can be used for attitude stabilization of a rigid body and we illustrate the behavior of the closed-loop system via simulation results.