A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems

Yoshio Ebihara, Tomomichi Hagiwara

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMI's are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMI's carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMI's are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMI's leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMI's enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.

Original languageEnglish
Pages (from-to)839-844
Number of pages6
JournalProceedings of the American Control Conference
Publication statusPublished - 2003
Externally publishedYes
Event2003 American Control Conference - Denver, CO, United States
Duration: Jun 4 2003Jun 6 2003

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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