On three generalizations of contraction

Eduardo D. Sontag, Michael Margaliot, Tamir Tuller

Research output: Contribution to journalConference articlepeer-review

6 Scopus citations


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 (US)
Article number7039618
Pages (from-to)1539-1544
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Issue numberFebruary
StatePublished - 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Control and Systems Engineering
  • Modeling and Simulation


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