ON THE ATTITUDE STABILIZATION OF RIGID SPACECRAFT

In this paper, we settle in the negative a longstanding problem concerning the existence of a smooth (static or dynamic) state variable feedback law locally asymptotically stabilizing a rigid spacecraft with two controls about a desired reference attitude. Modelling a spacecraft actuated by three thruster jets, one of which has failed, this well studied system is known to be locally reachable and locally asymptotically null controllable. We obtain our result as a corollary of a surprising result which asserts, for a class of nonlinear systems containing several examples of interest, that such a system is locally asymptotically stabilizable precisely when it can be linearized via state feedback transformations. We give a further result on the instability (in the sense of Lyapunov) of rigid spacecraft for certain feedback laws, but we are able to construct a feedback law locally asymptotically driving the closed-loop trajectories to a motion about the third principal axis. This law is derived using general principles comprising a nonlinear enhancement of root-locus design principles.