Self-sustained oscillations in discrete-time relay feedback systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909738249224192 |
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| author | Tong, Kang Grussler, Christian Chong, Michelle S. |
| author_facet | Tong, Kang Grussler, Christian Chong, Michelle S. |
| contents | We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the output has a single-peaked period. Under the assumption that the linear system is stable and has an impulse response that is strictly monotonically decreasing on its infinite support, we take a novel approach in using the framework of total positivity to address our main question. It is shown that unimodal self-oscillations can only exist if the number of positive and negative elements in a period coincides. Based on this result, we derive conditions for the existence of such oscillations, determine bounds on their periods, and address the question of uniqueness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-sustained oscillations in discrete-time relay feedback systems Tong, Kang Grussler, Christian Chong, Michelle S. Optimization and Control Systems and Control Dynamical Systems 34A34, 34C12, 93C55 We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the output has a single-peaked period. Under the assumption that the linear system is stable and has an impulse response that is strictly monotonically decreasing on its infinite support, we take a novel approach in using the framework of total positivity to address our main question. It is shown that unimodal self-oscillations can only exist if the number of positive and negative elements in a period coincides. Based on this result, we derive conditions for the existence of such oscillations, determine bounds on their periods, and address the question of uniqueness. |
| title | Self-sustained oscillations in discrete-time relay feedback systems |
| topic | Optimization and Control Systems and Control Dynamical Systems 34A34, 34C12, 93C55 |
| url | https://arxiv.org/abs/2504.05941 |