Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds

Olof Troeng

doi:10.1109/LCSYS.2020.3004297

Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds

Research output: Contribution to journal › Letter › peer-review

Abstract

We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility SDP and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks. Known results are also revisited using the proposed approach.

Original language	English
Pages (from-to)	583 - 586
Number of pages	4
Journal	IEEE Control Systems Letters
Volume	5
Issue number	2
DOIs	https://doi.org/10.1109/LCSYS.2020.3004297
Publication status	Published - 2021 Apr

Subject classification (UKÄ)

Control Engineering

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10.1109/LCSYS.2020.3004297

https://arxiv.org/abs/2007.05222

ScalableControl: Scalable Control of Interconnected Systems
Rantzer, A. (PI), Jouini, T. (Researcher), Agner, F. (Researcher), Troeng, O. (Researcher), Kergus, P. (Researcher), Pates, R. (Researcher), Kjellqvist, O. (Researcher), Renganathan, V. (Researcher), Wu, D. (Researcher) & Lindberg, J. (Researcher)
2019/09/01 → 2024/08/31
Project: Research

Cite this

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title = "Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds",

abstract = "We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility SDP and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks. Known results are also revisited using the proposed approach.",

author = "Olof Troeng",

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AU - Troeng, Olof

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AB - We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility SDP and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks. Known results are also revisited using the proposed approach.

U2 - 10.1109/LCSYS.2020.3004297

DO - 10.1109/LCSYS.2020.3004297

M3 - Letter

SN - 2475-1456

VL - 5

SP - 583

EP - 586

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

IS - 2

ER -

Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds

Abstract

Subject classification (UKÄ)

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Projects

ScalableControl: Scalable Control of Interconnected Systems

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