Switching through singularities

Asymptotic tracking is studied for systems which are not regular, that is the relative degree is not well defined. Hence the control law derived from exact input-output linearization has singularities in the state space. We propose a tracking control law which switches between an approximate tracking law close to the singularities, and an exact tracking law away from the singularities, and we study the applicability of this law based on the behavior of the system's zero dynamics at the switching boundary. The ball and beam example is used to motivate the study.