Stability analysis with dissipation inequalities and integral quadratic constraints

Peter Seiler

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108 Scopus citations


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 languageEnglish (US)
Article number6915700
Pages (from-to)1704-1709
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 1 2015

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


  • Integral quadratic constraint (IQC)
  • linear time-invariant (LTI)


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