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
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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 -