We study the dynamic behavior and stability of two connectedRayleigh beams that are subject to, in addition to two sensors andtwo actuators applied at the joint point, one of the actuators alsospecially distributed along the beams. We show that with thedistributed control employed, there is a set of generalizedeigenfunctions of the closed-loop system, which forms a Riesz basiswith parenthesis for the state space. Then both thespectrum-determined growth condition and exponential stability areconcluded for the system. Moreover, we show that the exponentialstability is independent of the location of the joint. The range ofthe feedback gains that guarantee the system to be exponentiallystable is identified.
