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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.21493 |
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| _version_ | 1866910922931437568 |
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| author | Zhou, Bin Zhang, Kai |
| author_facet | Zhou, Bin Zhang, Kai |
| contents | This paper addresses the stabilization of linear systems with multiple time-varying input delays. In scenarios where neither the exact delays information nor their bound is known, we propose a class of linear time-varying state feedback controllers by using the solution to a parametric Lyapunov equation (PLE). By leveraging the properties of the solution to the PLE and constructing a time-varying Lyapunov-Krasovskii-like functional, we prove that (the zero solution of) the closed-loop system is asymptotically stable. Furthermore, this result is extended to the observer-based output feedback case. The notable characteristic of these controllers is their utilization of linear time-varying gains. Furthermore, they are designed entirely independent of any knowledge of the time delays, resulting in controllers that are exceedingly easy to implement. Finally, a numerical example demonstrates the effectiveness of the proposed approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilization of linear systems with multiple unknown time-varying input delays by linear time-varying feedback Zhou, Bin Zhang, Kai Dynamical Systems This paper addresses the stabilization of linear systems with multiple time-varying input delays. In scenarios where neither the exact delays information nor their bound is known, we propose a class of linear time-varying state feedback controllers by using the solution to a parametric Lyapunov equation (PLE). By leveraging the properties of the solution to the PLE and constructing a time-varying Lyapunov-Krasovskii-like functional, we prove that (the zero solution of) the closed-loop system is asymptotically stable. Furthermore, this result is extended to the observer-based output feedback case. The notable characteristic of these controllers is their utilization of linear time-varying gains. Furthermore, they are designed entirely independent of any knowledge of the time delays, resulting in controllers that are exceedingly easy to implement. Finally, a numerical example demonstrates the effectiveness of the proposed approaches. |
| title | Stabilization of linear systems with multiple unknown time-varying input delays by linear time-varying feedback |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.21493 |