Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs

Yusuke Matsuda, Yoshio Ebihara, Tomomichi Hagiwara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

Original languageEnglish
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages2174-2179
Number of pages6
DOIs
Publication statusPublished - Dec 1 2009
Externally publishedYes
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: Dec 15 2009Dec 18 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period12/15/0912/18/09

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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  • Cite this

    Matsuda, Y., Ebihara, Y., & Hagiwara, T. (2009). Constructing a sequence of relaxation problems for robustness analysis of uncertain LTI systems via dual LMIs. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 2174-2179). [5399826] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399826