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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.10037 |
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| _version_ | 1866917479836549120 |
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| author | Mei, Zhan-Dong Tang, Lan-Xi |
| author_facet | Mei, Zhan-Dong Tang, Lan-Xi |
| contents | In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control. Four types of boundary interconnections are considered. In the absence of disturbances, a novel transformation is introduced to incorporate the PDE boundary control input into the ODE subsystem. Based on this transformation, a state feedback controller is designed to achieve exponential stability for both the ODE and PDE components. When internal uncertainties and external disturbances that match the control structure are present, a disturbance estimator is constructed. Utilizing this estimator, a Luenberger-type state observer is developed to reject the disturbances and exponentially stabilize the original system via an observer-based control scheme. Furthermore, the boundedness of the entire closed-loop system is rigorously established. Numerical simulations are provided to illustrate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stabilization for a Cascaded ODE-Wave Equation with Boundary Nonlinear Disturbances Mei, Zhan-Dong Tang, Lan-Xi Optimization and Control In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control. Four types of boundary interconnections are considered. In the absence of disturbances, a novel transformation is introduced to incorporate the PDE boundary control input into the ODE subsystem. Based on this transformation, a state feedback controller is designed to achieve exponential stability for both the ODE and PDE components. When internal uncertainties and external disturbances that match the control structure are present, a disturbance estimator is constructed. Utilizing this estimator, a Luenberger-type state observer is developed to reject the disturbances and exponentially stabilize the original system via an observer-based control scheme. Furthermore, the boundedness of the entire closed-loop system is rigorously established. Numerical simulations are provided to illustrate the theoretical results. |
| title | Stabilization for a Cascaded ODE-Wave Equation with Boundary Nonlinear Disturbances |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.10037 |