Robust and Gain-Scheduling ${\cal H}_2$ Control Techniques for LFT Uncertain and Parameter-Dependent Systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908820707475456 |
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| author | Wu, Fen |
| author_facet | Wu, Fen |
| contents | This paper addresses the robust ${\cal H}_2$ synthesis problem for linear fractional transformation (LFT) systems subject to structured uncertainty (parameter) and white-noise disturbances. By introducing an intermediate matrix variable, we derive convex synthesis conditions in terms of linear matrix inequalities (LMIs) that enable both robust and gain-scheduled controller design for parameter-dependent systems. The proposed framework preserves the classical white-noise and impulse-response interpretation of the ${\cal H}_2$ criterion while providing certified robustness guarantees, thereby extending optimal ${\cal H}_2$ control beyond the linear time-invariant setting. Numerical and application examples demonstrate that the resulting robust ${\cal H}_2$ controllers achieve significantly reduced conservatism and improved disturbance rejection compared with conventional robust ${\cal H}_\infty$-based designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08137 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust and Gain-Scheduling ${\cal H}_2$ Control Techniques for LFT Uncertain and Parameter-Dependent Systems Wu, Fen Systems and Control This paper addresses the robust ${\cal H}_2$ synthesis problem for linear fractional transformation (LFT) systems subject to structured uncertainty (parameter) and white-noise disturbances. By introducing an intermediate matrix variable, we derive convex synthesis conditions in terms of linear matrix inequalities (LMIs) that enable both robust and gain-scheduled controller design for parameter-dependent systems. The proposed framework preserves the classical white-noise and impulse-response interpretation of the ${\cal H}_2$ criterion while providing certified robustness guarantees, thereby extending optimal ${\cal H}_2$ control beyond the linear time-invariant setting. Numerical and application examples demonstrate that the resulting robust ${\cal H}_2$ controllers achieve significantly reduced conservatism and improved disturbance rejection compared with conventional robust ${\cal H}_\infty$-based designs. |
| title | Robust and Gain-Scheduling ${\cal H}_2$ Control Techniques for LFT Uncertain and Parameter-Dependent Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2602.08137 |