Riesz basis generation, eigenvalues distribution, and exponential stability for a euler-bernoulli beam with joint feedback control
نویسندگان
چکیده
منابع مشابه
Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients
This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler–Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition,...
متن کاملRiesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass
Using an abstract condition of Riesz basis generation of discrete operators in the Hilbert spaces, we show, in this paper, that a sequence of generalized eigenfunctions of an Euler– Bernoulli beam equation with a tip mass under boundary linear feedback control forms a Riesz basis for the state Hilbert space. In the meanwhile, an asymptotic expression of eigenvalues and the exponential stability...
متن کاملCoupled Linear Feedback and Sliding Model Control for a Serially Connected Euler-Bernoulli Beam
A system of serially connected string and Euler-Bernoulli beam with coupled linear feedback control and sliding model control is studied in the present paper. The system is formulated by partial differential equations with the boundary conditions. The eigenvalues and eigenfunctions of the system operator are discussed in the appropriate Hilbert spaces. A sliding model control is applied to the ...
متن کاملExponential stability of variable coefficients Rayleigh beams under boundary feedback controls: a Riesz basis approach
In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, sti9ness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a deta...
متن کاملRiesz Basis Property of Timoshenko Beams with Boundary Feedback Control
A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 2001
ISSN: 1988-2807,1139-1138
DOI: 10.5209/rev_rema.2001.v14.n1.17057