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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

Corresponding Author:[email protected]

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Yi Cheng
Bohai University
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Donal O'Regan
National University of Ireland
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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.
19 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
20 Apr 2021Submission Checks Completed
20 Apr 2021Assigned to Editor
26 Apr 2021Reviewer(s) Assigned
23 Aug 2021Review(s) Completed, Editorial Evaluation Pending
24 Aug 2021Editorial Decision: Revise Major
31 Aug 20211st Revision Received
31 Aug 2021Assigned to Editor
31 Aug 2021Submission Checks Completed
31 Aug 2021Reviewer(s) Assigned
09 Sep 2021Review(s) Completed, Editorial Evaluation Pending
09 Sep 2021Editorial Decision: Revise Minor
10 Sep 20212nd Revision Received
10 Sep 2021Submission Checks Completed
10 Sep 2021Assigned to Editor
10 Sep 2021Reviewer(s) Assigned
10 Sep 2021Review(s) Completed, Editorial Evaluation Pending
14 Sep 2021Editorial Decision: Accept
Feb 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 3 on pages 1488-1497. 10.1002/mma.7867