Robust performance analysis of uncertain LTI systems: Dual LMI approach and verifications for exactness

Yoshio Ebihara, Yusuke Onishi, Tomomichi Hagiwara

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

3 Citations (Scopus)

Abstract

This paper addresses robust performance analysis problems of LTI systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important role. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything directly if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution, which does exist if the primal LMI is infeasible. By pursuing this direction, in this paper, we provide a rank condition on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can readily be obtained. The key idea to derive these results comes from simultaneous diagonalizability property of commuting diagonalizable matrices. The block-moment matrix structure of the dual variable plays an essential role to make good use of this property.

Original languageEnglish
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages6304-6309
Number of pages6
DOIs
Publication statusPublished - 2007
Externally publishedYes
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

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

Conference

Conference46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

All Science Journal Classification (ASJC) codes

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

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  • Cite this

    Ebihara, Y., Onishi, Y., & Hagiwara, T. (2007). Robust performance analysis of uncertain LTI systems: Dual LMI approach and verifications for exactness. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 6304-6309). [4434124] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434124