On the Existence of Periodic Solutions with Applications to Extremum-Seeking
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910022182633472 |
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| author | Karafyllis, Iasson Krstic, Miroslav |
| author_facet | Karafyllis, Iasson Krstic, Miroslav |
| contents | This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the equivalence of the existence of a periodic solution and the existence of a bounded solution. The second result provides sufficient conditions for the existence and the stability of a periodic solution for a time-periodic dynamical system. Both results are applied to extremum seeking problems for a static output map with no plant dynamics and novel non-local results are provided without the use of averaging theorems and singular perturbation arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Existence of Periodic Solutions with Applications to Extremum-Seeking Karafyllis, Iasson Krstic, Miroslav Optimization and Control Systems and Control Dynamical Systems This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the equivalence of the existence of a periodic solution and the existence of a bounded solution. The second result provides sufficient conditions for the existence and the stability of a periodic solution for a time-periodic dynamical system. Both results are applied to extremum seeking problems for a static output map with no plant dynamics and novel non-local results are provided without the use of averaging theorems and singular perturbation arguments. |
| title | On the Existence of Periodic Solutions with Applications to Extremum-Seeking |
| topic | Optimization and Control Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2602.13615 |