Asymptotic output tracking through singular points for nonlinear systems: Stability, disturbance rejection and robustness

The problem of output tracking in the presence of singularities started by Hirschorn and Davis (1987) 2 is reexamined. A transformation which allows us to make a study of the closed‐loop stability of the nonlinear system is proposed. An error feedback control law relaxes the initial conditions imposed on the system and the function to be followed, obtaining asymptotic output tracking. A study of the singular tracking problem, when there exist disturbances or uncertainties in the dynamics, is also made. Again a stability analysis is carried out. Finally, the results obtained for the SISO case, to the MIMO case are extended.