loading page

Sector stability criteria for a nonlinear axial motion string system
  • Rui Wu,
  • Yi Cheng,
  • Donal O'Regan
Rui Wu
Changchun University of Finance and Economics
Author Profile
Yi Cheng
Bohai University
Author Profile
Donal O'Regan
National University of Ireland
Author Profile

Abstract

The paper investigates the exponential stability criterion for an axially moving string system driven by a nonlinear partial differential equation with nonlinear boundary feedback.The control criterion based on a sector condition contains a large class of nonlinearities, which is a negative feedback of the velocity at the right boundary of the moving string. By invoking nonlinear semigroup theory, the well-posedness result of the closed-loop system is verified under the sector criteria. Furthermore, a novel energy like function is constructed to establish the exponential stability of the closed-loop system by using a integral-type multiplier method and the generalized Gronwall-type integral inequality.

Peer review status:UNDER REVIEW

19 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
20 Apr 2021Assigned to Editor
20 Apr 2021Submission Checks Completed
26 Apr 2021Reviewer(s) Assigned