Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach

Sei Zhen Khong, Ian R. Petersen, Anders Rantzer

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

5 Scopus citations


Sufficient conditions for stability of feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. These extend existing results in the literature by exploiting the flexibility present at the static and infinite frequencies to reduce conservatism. Negative imaginary transfer functions with poles on the imaginary axis are accommodated using a recently generalised IQC-based robustness result. In particular, the negative imaginary property of systems is shown to give rise to IQCs on positive frequencies that are bounded away from zero and infinity. Additional quadratic conditions are introduced to take care of the IQCs near the DC and instantaneous gains of the systems.

Original languageEnglish (US)
Title of host publication2015 European Control Conference, ECC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9783952426937
StatePublished - Nov 16 2015
EventEuropean Control Conference, ECC 2015 - Linz, Austria
Duration: Jul 15 2015Jul 17 2015

Publication series

Name2015 European Control Conference, ECC 2015


OtherEuropean Control Conference, ECC 2015

Bibliographical note

Funding Information:
This work was supported by the Swedish Research Council through the LCCC Linnaeus centre and the Australian Research Council

Publisher Copyright:
© 2015 EUCA.


  • Negative imaginary systems
  • feedback stability
  • integral quadratic constraints


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