Abstract
This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism.
| Original language | English (US) |
|---|---|
| Article number | 6915700 |
| Pages (from-to) | 1704-1709 |
| Number of pages | 6 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 60 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 1 2015 |
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Keywords
- Integral quadratic constraint (IQC)
- linear time-invariant (LTI)
Cite this
Stability analysis with dissipation inequalities and integral quadratic constraints. / Seiler, Peter.
In: IEEE Transactions on Automatic Control, Vol. 60, No. 6, 6915700, 01.06.2015, p. 1704-1709.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stability analysis with dissipation inequalities and integral quadratic constraints
AU - Seiler, Peter
PY - 2015/6/1
Y1 - 2015/6/1
N2 - This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism.
AB - This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism.
KW - Integral quadratic constraint (IQC)
KW - linear time-invariant (LTI)
UR - http://www.scopus.com/inward/record.url?scp=84930657546&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84930657546&partnerID=8YFLogxK
U2 - 10.1109/TAC.2014.2361004
DO - 10.1109/TAC.2014.2361004
M3 - Article
AN - SCOPUS:84930657546
VL - 60
SP - 1704
EP - 1709
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 6
M1 - 6915700
ER -