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

Tamas Peni, Harald Pfifer

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publication2015 European Control Conference, ECC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3091-3096
Number of pages6
ISBN (Electronic)9783952426937
DOIs
StatePublished - Nov 16 2015
EventEuropean Control Conference, ECC 2015 - Linz, Austria
Duration: Jul 15 2015Jul 17 2015

Publication series

Name2015 European Control Conference, ECC 2015

Other

OtherEuropean Control Conference, ECC 2015
CountryAustria
CityLinz
Period7/15/157/17/15

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