On three generalizations of contraction

Eduardo D. Sontag, Michael Margaliot, Tamir Tuller

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We introduce three forms of generalized contraction (GC). Roughly speaking, these are motivated by allowing contraction to take place after small transients in time and/or amplitude. Indeed, contraction is usually used to prove asymptotic properties, like convergence to an attractor or entrainment to a periodic excitation, and allowing initial transients does not affect this asymptotic behavior. We provide sufficient conditions for GC, and demonstrate their usefulness using examples of systems that are not contractive, with respect to any norm, yet are GC.

Original languageEnglish
Title of host publication53rd IEEE Conference on Decision and Control,CDC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479977468
StatePublished - 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: 15 Dec 201417 Dec 2014

Publication series

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


Conference2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/TerritoryUnited States
CityLos Angeles


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