Boundary feedback stabilization of the sine-Gordon equation without velocity feedback

This paper is concerned with the system governed by the sine-Gordon equation without damping. From a practical point of view, velocity may not be measured precisely. The global stabilization of the system governed by the sine-Gordon equation without damping is investigated in the case where any velocity feedback is not available. In such cases only position feedback cannot asymptotically stabilize the system. A parallel compensator is effective. The stabilizer is constructed by a proportional controller for the augmented system which consists of the controlled system and a parallel compensator. The asymptotic stability of the closed-loop system is proved.