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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19637903 |
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| _version_ | 1866902074629816320 |
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| author | Zhang, Jincheng |
| author_facet | Zhang, Jincheng |
| contents | <p><span>This paper proposes a novel robust matrix constraint modeling method that unifies the linear matrix inequality (LMI) structure with Box uncertainty sets, constructing a unified expression for describing the positive semidefiniteness of matrices under parameter perturbations. Traditional LMI methods primarily handle deterministic or affine parameter systems, while Box uncertainty sets can characterize the worst-case scenario where parameters vary independently within interval boundaries. By introducing "vertex matrix decomposition mapping" and "worst-case boundary projection operator," this paper derives an equivalent verifiable form of the robust linear matrix inequality (RBLMI), thus transforming the infinite constraint problem into a set of finite positive semidefinite matrix constraints. This method has potential applications in robust control, optimization theory, and stability analysis of machine learning models.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19637903 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Robust Box-Linear Matrix Inequalities: A Unified Spectral Worst-Case Framework for Convex Uncertainty Modeling Zhang, Jincheng <p><span>This paper proposes a novel robust matrix constraint modeling method that unifies the linear matrix inequality (LMI) structure with Box uncertainty sets, constructing a unified expression for describing the positive semidefiniteness of matrices under parameter perturbations. Traditional LMI methods primarily handle deterministic or affine parameter systems, while Box uncertainty sets can characterize the worst-case scenario where parameters vary independently within interval boundaries. By introducing "vertex matrix decomposition mapping" and "worst-case boundary projection operator," this paper derives an equivalent verifiable form of the robust linear matrix inequality (RBLMI), thus transforming the infinite constraint problem into a set of finite positive semidefinite matrix constraints. This method has potential applications in robust control, optimization theory, and stability analysis of machine learning models.</span></p> |
| title | Robust Box-Linear Matrix Inequalities: A Unified Spectral Worst-Case Framework for Convex Uncertainty Modeling |
| url | https://doi.org/10.5281/zenodo.19637903 |