Arbitrarily fast exponentially stabilizing controller for multi-input, persistently exciting singular control gain systems

We develop a new technique for stabilizing multi-input linear systems with unstable drift and time-varying, singular gains on the control. The results presented here assume the control gain to be sufficiently smooth and satisfy a persistence of excitation condition. A novel persistence filter construction is proposed that enables a non-trivial generalization of the authors’ previous result on stabilization of single-input linear systems. The paper also presents an adaptive control extension of the main result.