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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
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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.

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