Determining "mixedness" and an application of finite-gain stability results to "mixed" system interconnections

Wynita M. Griggs, Brian D.O. Anderson, Robert N. Shorten

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

2 Citations (Scopus)


A loss of passivity in the face of certain frequency dynamics (eg: high frequency dynamics) given an otherwise passive system leads to the notion of a "mixed" system. A "mixed" system is one that has a concept of small gain associated with it over those frequency intervals where passivity is lost. In this paper, a test for determining "mixedness" for linear, time-invariant systems is provided and several finitegain stability results for interconnections of such systems are presented. The "mixedness" test involves examining the spectral characteristics of two Hamiltonian matrices, one associated with the passive aspects of the system and one associated with the notion of small gain. The finite-gain stability results are derived using a dissipative systems framework.

Original languageEnglish
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages6
ISBN (Print)9781424477456
Publication statusPublished - 2010
Externally publishedYes
EventIEEE Conference on Decision and Control 2010 - Atlanta, United States of America
Duration: 15 Dec 201017 Dec 2010
Conference number: 49th (Proceedings)

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216


ConferenceIEEE Conference on Decision and Control 2010
Abbreviated titleCDC 2010
Country/TerritoryUnited States of America
Internet address

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