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

Stabilizing Controllers for Multi-Input, Singular Control Gain Systems