Switching through singularities

Asymptotic tracking is studied for systems which are not regular, that is, the relative degree is not well defined. For these systems, the input–output linearizing control law has singularities. We propose a tracking control law which switches between an approximate tracking law (Hauser et al., IEEE Trans. Automat. Control 37 (3) (1992) 392–398) 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. As in Hauser et al. (IEEE Trans. Automat. Control 37 (3) (1992) 392–398), the ball and beam example is used to motivate the study.