Period-aware asymptotic gain with application to a periodically forced synchronization circuit
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917362098241536 |
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| author | Ponomarev, Anton Gröll, Lutz Hagenmeyer, Veit |
| author_facet | Ponomarev, Anton Gröll, Lutz Hagenmeyer, Veit |
| contents | The classical asymptotic gain (AG) is a concept known from the input-to-state stability theory. Given a uniform input bound, AG estimates the asymptotic bound of the output. Sometimes, however, more information is known about the input than just a bound. In this paper we consider the case of a periodic input. Under the assumption that the system converges to a periodic solution, we introduce a new gain, called period-aware asymptotic gain (PAG), which employs periodicity to enable a sharper asymptotic estimation of the output. Since the PAG can distinguish between short-period ("high-frequency") and long-period ("low-frequency") signals, it is able to rigorously quantify such properties as bandwidth, resonant behavior, and high-frequency damping. We discuss how the PAG can be computed and illustrate it with a numerical example from the field of power electronics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24600 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Period-aware asymptotic gain with application to a periodically forced synchronization circuit Ponomarev, Anton Gröll, Lutz Hagenmeyer, Veit Optimization and Control Systems and Control The classical asymptotic gain (AG) is a concept known from the input-to-state stability theory. Given a uniform input bound, AG estimates the asymptotic bound of the output. Sometimes, however, more information is known about the input than just a bound. In this paper we consider the case of a periodic input. Under the assumption that the system converges to a periodic solution, we introduce a new gain, called period-aware asymptotic gain (PAG), which employs periodicity to enable a sharper asymptotic estimation of the output. Since the PAG can distinguish between short-period ("high-frequency") and long-period ("low-frequency") signals, it is able to rigorously quantify such properties as bandwidth, resonant behavior, and high-frequency damping. We discuss how the PAG can be computed and illustrate it with a numerical example from the field of power electronics. |
| title | Period-aware asymptotic gain with application to a periodically forced synchronization circuit |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.24600 |