Work

The Riesz basisness of the eigenfunctions and eigenvectors connected to the stability problem of a fluid‐conveying tube with boundary control

Year: 2024

Type: article

Abstract: In the present paper we study the stability problem for a stretched tube conveying fluid with boundary control. The abstract spectral problem concerns operator pencils of the forms taking values in different Hilbert product spaces. Thorough analysis is made of the existence, location, multiplicities, and asymptotics of eigenvalues in the complex plane and Riesz basisness of the corresponding eigenfunctions and eigenvectors. Well‐posedness of the closed‐loop system represented by the initial‐value problem for the abstract equation is established in the framework of ‐semigroups as well as expansions of the solutions in terms of eigenvectors and stability of the closed‐loop system. For the parameters of the problem we give new regions, larger than those in the literature, in which a stretched tube with flow, simply supported at one end, with a boundary controller applied at the other end, can be exponentially stabilised.

Source: ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

DOI: 10.1002/zamm.202300455

Authors: Mahyar Mahinzaeim, Gen Qi Xu, Xiao Xuan Feng

Institutions: Hochschule Aalen, Tianjin University, Hebei Normal University of Science and Technology

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,300

Funders: Newcastle University, National Natural Science Foundation of China