Abstract
In this paper, we address the robust H2 performance analysis problems of linear time-invariant polytopic-type uncertain systems. To obtain numerically verifiable and less conservative analysis conditions, we employ polynomially parameter-dependent Lyapunov functions (PPDLFs) to assess the robust H2 performance and give a sufficient condition for the existence of such PPDLFs in terms of finitely many linear matrix inequalities (LMIs). The resulting LMI conditions turn out to be a natural extension of those known as extended or dilated LMIs in the literature, where the PDLFs employed were restricted to those depending affinely on the uncertain parameters. It is shown that, by increasing the degree of PPDLFs, we can obtain more accurate (no more conservative) analysis results at the expense of increased computational burden. Exactness of the proposed analysis conditions as well as their computational complexity will be examined through numerical experiments.
| Original language | English |
|---|---|
| Title of host publication | ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts |
| Pages | 435-440 |
| Number of pages | 6 |
| Edition | PART 1 |
| Publication status | Published - Dec 1 2006 |
| Event | 5th IFAC Symposium on Robust Control Design, ROCOND'06 - Toulouse, France Duration: Jul 5 2006 → Jul 7 2006 |
Publication series
| Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
|---|---|
| Number | PART 1 |
| Volume | 5 |
| ISSN (Print) | 1474-6670 |
Conference
| Conference | 5th IFAC Symposium on Robust Control Design, ROCOND'06 |
|---|---|
| Country | France |
| City | Toulouse |
| Period | 7/5/06 → 7/7/06 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
Cite this
Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions. / Ebihara, Yoshio; Peaucelle, Dimitri; Arzelier, Denis; Hagiwara, Tomomichi.
ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts. PART 1. ed. 2006. p. 435-440 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 5, No. PART 1).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions
AU - Ebihara, Yoshio
AU - Peaucelle, Dimitri
AU - Arzelier, Denis
AU - Hagiwara, Tomomichi
PY - 2006/12/1
Y1 - 2006/12/1
N2 - In this paper, we address the robust H2 performance analysis problems of linear time-invariant polytopic-type uncertain systems. To obtain numerically verifiable and less conservative analysis conditions, we employ polynomially parameter-dependent Lyapunov functions (PPDLFs) to assess the robust H2 performance and give a sufficient condition for the existence of such PPDLFs in terms of finitely many linear matrix inequalities (LMIs). The resulting LMI conditions turn out to be a natural extension of those known as extended or dilated LMIs in the literature, where the PDLFs employed were restricted to those depending affinely on the uncertain parameters. It is shown that, by increasing the degree of PPDLFs, we can obtain more accurate (no more conservative) analysis results at the expense of increased computational burden. Exactness of the proposed analysis conditions as well as their computational complexity will be examined through numerical experiments.
AB - In this paper, we address the robust H2 performance analysis problems of linear time-invariant polytopic-type uncertain systems. To obtain numerically verifiable and less conservative analysis conditions, we employ polynomially parameter-dependent Lyapunov functions (PPDLFs) to assess the robust H2 performance and give a sufficient condition for the existence of such PPDLFs in terms of finitely many linear matrix inequalities (LMIs). The resulting LMI conditions turn out to be a natural extension of those known as extended or dilated LMIs in the literature, where the PDLFs employed were restricted to those depending affinely on the uncertain parameters. It is shown that, by increasing the degree of PPDLFs, we can obtain more accurate (no more conservative) analysis results at the expense of increased computational burden. Exactness of the proposed analysis conditions as well as their computational complexity will be examined through numerical experiments.
UR - http://www.scopus.com/inward/record.url?scp=80051595031&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051595031&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:80051595031
SN - 9783902661104
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 435
EP - 440
BT - ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts
ER -