Ultimate state boundedness of underactuated spacecraft subject to an unmatched disturbance

Ultimate state boundedness for underactuated spacecraft subject to large non-matched disturbances
is attained. First, non-smooth time-invariant state feedback control laws that
make the origin asymptotically stable are obtained. Then, the controller is extended to
make the closed-loop system globally uniformly ultimately bounded under the following
conditions: 1) the disturbances acting on the directly actuated states are known and 2) the
disturbance acting on the unactuated state is bounded and its profile need not be known.
Finally, numerical simulations are presented to verify the analytical results. A large step disturbance
is considered, and it is shown that the proposed controller makes the closed-loop
system globally uniformly ultimately bounded. The proposed method is rather general and
can be extended to other systems.