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Input-to-state stabilization of an ODE-wave system with disturbances

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Abstract

In this paper, we consider the input-to-state stabilization of an ODE-wave feedback-connection system with Neumann boundary control, where the left end displacement of the wave equation enters the ODE, while the output of the ODE is fluxed into boundary of the wave equation. The disturbance is appeared as a nonhomogeneous term in the ODE. Based on the backstepping approach, a state feedback control law is designed to guarantee the exponential input-to-state stability of the closed-loop system. The resulting closed-loop system has been shown to be well-posed by the semigroup approach. Moreover, we construct an exponentially convergent state observer based on which an output feedback control law is obtained, and the closed-loop system is proved to be input-to-state stable.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Yu-Long Zhang & Jun-Min Wang

  2. China State Key Laboratory of Power Systems and Generation Equipment, Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China

    Donghai Li

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  1. Yu-Long Zhang
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  2. Jun-Min Wang
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  3. Donghai Li
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Correspondence to Jun-Min Wang.

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Published in the topical collection Input-to-state stability for infinite-dimensional systems

This work is partly supported by the National Natural Science Foundation of China with Grant/Award Number: 61673061.

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Zhang, YL., Wang, JM. & Li, D. Input-to-state stabilization of an ODE-wave system with disturbances. Math. Control Signals Syst. 32, 489–515 (2020). https://doi.org/10.1007/s00498-020-00266-8

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  • DOI: https://doi.org/10.1007/s00498-020-00266-8

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