A New Approach to the Stabilization of a Rayleigh Beam Using Collocated Control and Observation

A two-connected Rayleigh beam with two actuators and sensors at joint point and one distributed control is studied. It is shown that the closed-loop system is a Riesz spectral system, from which both the spectral-determined growth condition and exponential stability are concluded. Moreover, the exponential stability is shown to be robust on the location of the joint, and the range of the feedback gains that guarantee the system to be exponential stable is also identified qualitatively.