Nonlinear Feedback Stabilization of a Rotating Body-Beam Without Damping

This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping. The feedback law proposed hereother end. We assume that there is no damping. The feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a consists of a nonlinear control torque applied to the rigid body and either a nonlinear boundary control moment or a nonlinear boundary control force or both nonlinear boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the which insures the exponential decay of the beam vibrations, extends the linear case studied by Laousy et al. to a more general class of controls. This new class of controls is in particular of the interest to be robust

Stabilisation d'une équation de vibrations

Cet article traite la stabilisation frontière d'une équation de vibrations. On démontre que le système peut être stabilisé fortement ou exponentiellement par des feedbacks frontières non linéaires

Asymptotic behavior of Kawahara equation with memory effect

In this work, we are interested in a detailed qualitative analysis of the Kawahara equation, a model that has numerous physical motivations such as magneto-acoustic waves in a cold plasma and gravity waves on the surface of a heavy liquid. First, we design a feedback law, which combines a damping control and a finite memory term. Then, it is shown that the energy associated with this system exponentially decays.Comment: 20 pages. Comments are welcom

Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity

This paper deals with feedback stabilization of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the rigid body rotates with a nonconstant angular velocity. To stabilize this system, we propose a feedback law which consists of a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. Then it is shown that the closed loop system is well posed and exponentially stable provided that the actuators, which generate the boundary controls, satisfy some classical assumptions and the angular velocity is smaller than a critical one

Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System

This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. Subsequently, we deal with the eigenvalue problem of the system. More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded. Finally, the theoretical findings are validated via a set of numerical results