Integral quadratic constraint theorem: A topological separation approach

Joaquin Carrasco, Peter Seiler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


This paper concerns the input/output stability of two systems in closed-loop where stability is ensured by using open-loop properties of each subsystem. The literature is divided into consideration of time-domain and frequency-domain conditions. A complete time-domain approach is given by dissipative and topological separation theory, where both conditions are given in the time-domain. On the other hand, the frequency-domain integral quadratic constraints (IQCs) framework uses only frequency-domain conditions. Between both extremes, the classical multiplier approach and the time-domain IQC framework can be seen as hybrid versions where one condition is tested in the time-domain and other condition is tested in the frequency-domain. The time-domain is more natural for nonlinear systems, and subsystems may be unbounded in time-domain analysis. However, the frequency-domain has two advantages: firstly if one block is linear, then frequency-domain analysis leads to elegant graphical and/or LMI conditions; secondly noncausal multipliers can be used. Recently the connection between frequency domain IQCs and dissipativity has been studied. Here we use graph separation results to provide a unifying framework. In particular we show how a recent factorization result establishes a straightforward link, completing an analysis suggested previously. This factorization leads to a simple and insightful dissipative condition to analyse stability of the feedback interconnection.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479978861
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other54th IEEE Conference on Decision and Control, CDC 2015

Bibliographical note

Publisher Copyright:
© 2015 IEEE.


  • Frequency-domain analysis
  • Linear systems
  • Nonlinear systems
  • Stability analysis
  • Standards
  • Time-domain analysis
  • Transfer functions


Dive into the research topics of 'Integral quadratic constraint theorem: A topological separation approach'. Together they form a unique fingerprint.

Cite this