Input-state matching under piecewise constant control for systems on matrix Lie groups

The constructive controllability problem under piecewise constant control is discussed for systems evolving on matrix Lie groups. Two approaches are followed: an indirect one, in which a continuous time control is matched by a multi-rate sampled data controller ensuring coincidence at the sampling instants and a direct one, in which a digital point to point maneuver is designed. Simulations are performed to compare the continuous and digital approaches.