On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback

Abstract

Abstract.We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified.Mathematics Subject Classification. 93C20, 93C25, 35J10, 47E05

Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

“…where u xxt is the so-called structural damping. For further references on the Rayleigh beam model, we can refer the readers to the articles [3,4,11,16,17,20,21,23].…”

Pointwise feedback stabilization of an Euler-Bernoulli beam in observations with time delay

“…The general model of serially connected Euler-Bernoulli beams with joint linear feedback control was proposed in 1980s [8]. Later on many efforts have been made to study the pointwise feedback control stabilization for two connected beam equations, see for example [1,2,4,5,6,7,9,10,19,22,25] and the references therein.…”