Stabilizing controllers for multi-input, singular control gain systems

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 rely on a non-triviality assumption on the gain signal namely “persistence of excitation”. The control design is based on a novel persistence filter construction involving the singular control gain. This work extends 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.