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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 4
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Articles

Stabilization of serially connected hybrid PDE–ODE system with unknown external disturbances

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Pages 718-734 | Received 25 Feb 2017, Accepted 31 Oct 2017, Published online: 12 Nov 2017
 

ABSTRACT

The anti-disturbance stabilization problem of a kind of serially connected hybrid PDE–ODE system is considered. The system is constituted by n wave equations with n point masses at joint nodes and the free end, where the unknown disturbances exist. We stabilize the system by designing the nonlinear pointwise feedback control laws, in which the technique of sliding-mode control is employed to reject those disturbances. The well-posedness of the corresponding nonlinear closed-loop system is proved based on the theory of nonlinear maximal monotone operators. The exponential stability of the closed-loop system is further obtained. Finally, some numerical simulations are given to show the effectiveness of the control design proposed in this paper.

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Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Natural Science Foundation of China [grant number 61573252], [grant number 61174080].

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