摘要：AbstractWe study a PDE based linearized model for the vertical motion of a solid floating at the free surface of a shallow viscous fluid. The solid is controlled by a vertical force exerted via an actuator. This force is the input of the system, whereas the output is the distance from the solid to the bottom. The first novelty we bring in is that we prove that the governing equations define a well-posed linear system. This is done by considering adequate function spaces and convenient operators between them. Another contribution of this work is establishing that the system is input-output stable. To this aim, we give an explicit form of the transfer function and we show that it lies in the Hardy spaceH∞of the right-half plane.
关键词：KeywordsWell-posed systemsinput-output stabilitytransfer functioninfinite dimensional systems
