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PreprintCC BY-NC-ND 4.0arXiv

On the IQC and SRG Frameworks: Equivalences and Converse Results

  • Sebastiaan van den Eijnden
  • Chao Chen
  • Sei Zhen Khong
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Abstract

Integral quadratic constraints (IQCs) and scaled relative graphs (SRGs) are two prominent frameworks for analyzing feedback systems. Although both frameworks are rooted in the same graph separation principle, a general characterization of their relationship has remained unavailable. This paper establishes conditions under which the IQC- and SRG frameworks are equivalent. To this end, we introduce two new classes of systems, termed disjunctive and conjunctive systems, which are respectively characterized by unions and intersections of quadratic input-output constraints. Under structural assumptions, we prove equivalence between the IQC and SRG frameworks for these system classes. By exploiting this equivalence, we develop novel IQC- and SRG-based converse stability results for linear and nonlinear systems. Our results accommodate multiple quadratic constraints, extending well-known converse results in robust control beyond the single-constraint setting.

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Cite

BibTeXRIS
BibTeX
@misc{eijnden2026frameworks,
  title = {{On the IQC and SRG Frameworks: Equivalences and Converse Results}},
  author = {Sebastiaan van den Eijnden and Chao Chen and Sei Zhen Khong},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04593},
  eprint = {2611.04593},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04593},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the IQC and SRG Frameworks: Equivalences and Converse Results
AU  - Sebastiaan van den Eijnden
AU  - Chao Chen
AU  - Sei Zhen Khong
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04593
UR  - https://arxiv.org/abs/2611.04593
AB  - Integral quadratic constraints (IQCs) and scaled relative graphs (SRGs) are two prominent frameworks for analyzing feedback systems. Although both frameworks are rooted in the same graph separation principle, a general characterization of their relationship has remained unavailable. This paper establishes conditions under which the IQC- and SRG frameworks are equivalent. To this end, we introduce two new classes of systems, termed disjunctive and conjunctive systems, which are respectively characterized by unions and intersections of quadratic input-output constraints. Under structural assumptions, we prove equivalence between the IQC and SRG frameworks for these system classes. By exploiting this equivalence, we develop novel IQC- and SRG-based converse stability results for linear and nonlinear systems. Our results accommodate multiple quadratic constraints, extending well-known converse results in robust control beyond the single-constraint setting.
ER  -