Analysis of large scale parameter-varying systems by using scaled diagonal dominance

Tamas Peni; Harald Pfifer

doi:10.1109/ECC.2015.7331008

Analysis of large scale parameter-varying systems by using scaled diagonal dominance

Tamas Peni, Harald Pfifer

Aerospace Engineering and Mechanics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

It has been recognized recently that semidefinite optimization problems (SDP) can be cast into second order cone programs (SOCP) by replacing the positive definiteness constraints with stronger, scaled diagonal dominance (SDD) conditions. Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large dimensional problems more efficiently. However, scaled diagonal dominant matrices form only a subset of the positive definite matrices. Hence, the new problem formulation results in more conservative solutions. This paper analyses the efficiency and conservativeness of the SDD formulation on two particular problems: the stability analysis and induced L₂ gain computation for linear parameter-varying systems. In the paper some important features of the SDD formulation are revealed and numerical examples are provided to demonstrate the efficiency of the approach.

Original language	English (US)
Title of host publication	2015 European Control Conference, ECC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3091-3096
Number of pages	6
ISBN (Electronic)	9783952426937
DOIs	https://doi.org/10.1109/ECC.2015.7331008
State	Published - Nov 16 2015
Event	European Control Conference, ECC 2015 - Linz, Austria Duration: Jul 15 2015 → Jul 17 2015

Publication series

Name	2015 European Control Conference, ECC 2015

Other

Other	European Control Conference, ECC 2015
Country/Territory	Austria
City	Linz
Period	7/15/15 → 7/17/15

Bibliographical note

Publisher Copyright:
© 2015 EUCA.

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10.1109/ECC.2015.7331008

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Analysis of large scale parameter-varying systems by using scaled diagonal dominance. / Peni, Tamas; Pfifer, Harald.
2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 3091-3096 7331008 (2015 European Control Conference, ECC 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Peni, T & Pfifer, H 2015, Analysis of large scale parameter-varying systems by using scaled diagonal dominance. in 2015 European Control Conference, ECC 2015., 7331008, 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 3091-3096, European Control Conference, ECC 2015, Linz, Austria, 7/15/15. https://doi.org/10.1109/ECC.2015.7331008

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AB - It has been recognized recently that semidefinite optimization problems (SDP) can be cast into second order cone programs (SOCP) by replacing the positive definiteness constraints with stronger, scaled diagonal dominance (SDD) conditions. Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large dimensional problems more efficiently. However, scaled diagonal dominant matrices form only a subset of the positive definite matrices. Hence, the new problem formulation results in more conservative solutions. This paper analyses the efficiency and conservativeness of the SDD formulation on two particular problems: the stability analysis and induced L2 gain computation for linear parameter-varying systems. In the paper some important features of the SDD formulation are revealed and numerical examples are provided to demonstrate the efficiency of the approach.

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Analysis of large scale parameter-varying systems by using scaled diagonal dominance

Abstract

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