Comments on "Nonlinear output feedback control of dynamically positioned ships using vectorial observer backstepping"

The decomposition of nonlinear output feedback control into an observer and a state feedback control is an open problem. A solution for dynamic positioning of ships has been proposed in 1] and 2], where an observer-based back-stepping method is used. This note points out that the observer design in 1] and 2] does not cover unstable ship dynamics and suggests a remedy for an extended class of ships. The proof for the nonlinear observer used in the design in 1] and 2] only applies to ships with stable sway-yaw dynamics. In 1] and 2] an example concerning thruster assisted mooring of a tanker is given, which does not fullll the needed stability properties, so an extension to this case is highly motivated. We propose a method to extend the results, under a de-tectability condition. This condition implies stable surge dynamics, which is a natural assumption for ships.