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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/2603.03929 |
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| _version_ | 1866910040459313152 |
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| author | Grosso, Maxime Riedinger, Pierre Daafouz, Jamal Pierfederici, Serge Idrissi, Hicham Janati Lapôtre, Blaise |
| author_facet | Grosso, Maxime Riedinger, Pierre Daafouz, Jamal Pierfederici, Serge Idrissi, Hicham Janati Lapôtre, Blaise |
| contents | This paper develops a harmonic-domain framework for systems with variable fundamental frequency. A variable-frequency sliding Fourier decomposition is introduced in the phase domain, together with necessary and sufficient conditions for time- domain realizability. An exact harmonic-domain differential model is derived for general nonlinear systems under variable frequency, without assumptions on the frequency variation. An explicit parameter-varying approximation is then obtained, along with a tight error bound expressed in terms of local relative frequency variation, providing a non-conservative validity criterion and clarifying the limitations of classical heuristics. A main result shows that, for linear phase-periodic systems with affine frequency dependence, stability analysis and control synthesis can be carried out without approximation and without assumptions on the frequency variation, provided the frequency evolves within a prescribed interval. As a consequence, both problems reduce to harmonic Lyapunov inequalities evaluated at the two extreme frequency values, yielding a convex LMI characterization. The framework is illustrated on a variable-speed permanent magnet synchronous motor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harmonic Modeling and Control under Variable-Frequency Grosso, Maxime Riedinger, Pierre Daafouz, Jamal Pierfederici, Serge Idrissi, Hicham Janati Lapôtre, Blaise Systems and Control This paper develops a harmonic-domain framework for systems with variable fundamental frequency. A variable-frequency sliding Fourier decomposition is introduced in the phase domain, together with necessary and sufficient conditions for time- domain realizability. An exact harmonic-domain differential model is derived for general nonlinear systems under variable frequency, without assumptions on the frequency variation. An explicit parameter-varying approximation is then obtained, along with a tight error bound expressed in terms of local relative frequency variation, providing a non-conservative validity criterion and clarifying the limitations of classical heuristics. A main result shows that, for linear phase-periodic systems with affine frequency dependence, stability analysis and control synthesis can be carried out without approximation and without assumptions on the frequency variation, provided the frequency evolves within a prescribed interval. As a consequence, both problems reduce to harmonic Lyapunov inequalities evaluated at the two extreme frequency values, yielding a convex LMI characterization. The framework is illustrated on a variable-speed permanent magnet synchronous motor. |
| title | Harmonic Modeling and Control under Variable-Frequency |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2603.03929 |