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This paper discusses the design of a combined backstepping/Lyapunov controller for the attitude, velocity and height control of an unmanned, unstable, fin-less airship. As the airship actuation has more degrees of freedom than the motion controlled, the controller includes a quadratic optimization algorithm to find the optimal thruster commands. The control law developed provides attitude and velocity control for the entire airship flight regime, i.e., hover, vertical ascent and descent as well as cruise, all with a single controller. Controller performance is first verified using a simulation that includes detailed modeling of sensor noise, computational delays and actuation dynamics. Subsequently, the controller is tested in outdoor flight tests. The controller has been found to perform well both in simulation and flight tests. The controller parameters were identical in simulation and flight test demonstrating the high fidelity of the simulation.