How to find a minimum phase output in the exact tracking problem for the nonminimum phase underactuated surface ship

This paper shows how to choose a suitable output, different from the usual ship center of mass, transforming a non-minimum phase problem in a problem with a stable internal dynamic. More precisely, we choose as output a point P, placed on the ship principal symmetry axis, in front of the ship at a distance p from the center of mass. We show that the exact tracking problem for a smooth reference trajectory γ always admits a solution for this particular output and that the resulting internal dynamics are stable, provided that ρ is sufficiently large and the reference curve γ is such that ||γ̇|| does not vary too much and ||γ̈||, ||γ̇̈|| are sufficiently small. Moreover, an asymptotic stabilization result is proven.