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The nonlinear terms of the ship's course-keeping nonlinear systemare in the special forms. Based on this, a full-order state observer design method is presented. The parameters of the observer are computed by Matlab LMI toolbox. Observer backstepping method can be used to design the output feedback controller for the ship's course-keeping systems and global boundedness of all the states of the system can be guaranteed. Simulation results on a far-going experimental ship named `YULONG' are presented to validate the proposed controller.