This paper presents a successful graphical technique for finding all discrete-time proportional integral derivative (PID) controllers that satisfy a robust stability constraint for heading control of a 2 meter autonomous sailing vessel. This problem is solved by finding all achievable discrete time PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. The bilinear transformation is used to describe the discrete time PID controllers. The discrete-time model of the vessel is identified from a sampled data system with uncertain communication delay. Experimental data taken from this vessel at the U. S. Coast Guard Academy is used to demonstrate the application of this methodology.