  This paper proposes a new methodology for design of a stabilizing control law
for multi-input linear systems with time-varying, singular gains on the
control. The results presented here assume the control gain to satisfy
persistence of excitation which is a necessary condition for existence of
stabilizing controllers in the presence of unstable drift. This work involves a
novel persistence filter construction and provides a significant extension to
the authors' previous result on stabilization of single-input linear systems
with time-varying singular gains. An application to underactuated spacecraft
stabilization is shown which illustrates the interesting features of the
time-varying control design in stabilization of nonlinear dynamical systems.
Finally, the development of an observer counterpart of these results is
presented in the presence of multiple-outputs subject to singular measurement
gains.
