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arXiv · 2602.08137

Robust and Gain-Scheduling ${\cal H}_2$ Control Techniques for LFT Uncertain and Parameter-Dependent Systems

Fen Wu
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Abstract

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.

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BibTeXRIS

Fen Wu. 2026-02-08. Robust and Gain-Scheduling ${\cal H}_2$ Control Techniques for LFT Uncertain and Parameter-Dependent Systems. https://arxiv.org/abs/2602.08137

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