Approximate distributed controllability of nonlocal Rayleigh beam

Document Type : Research Paper

Authors

1 School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran.

2 School of Engineering, Damghan University, Damghan, Iran.

Abstract

This paper investigates the distributed controllability of nonlocal Rayleigh beam. The mathematical problem is formulated as an abstract differential equation. It is shown that a sequence of eigenfunction of nonlocal Rayleigh beam forms Riesz basis. Based on Riesz basis properties and theory of abstract differential equation, it is proved that a vibrating nonlocal Rayleigh beam is approximately controllable under suitable distributed control force while it is not exponentially stable.

Keywords


Volume 9, Issue 1
January 2021
Pages 180-186
  • Receive Date: 13 October 2018
  • Revise Date: 14 September 2019
  • Accept Date: 21 September 2019
  • First Publish Date: 01 January 2021