@INPROCEEDINGS{14cdc_margaliot_sontag_tuller_cast,
   AUTHOR       = {E.D. Sontag and M. Margaliot and T. Tuller},
   BOOKTITLE    = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014},
   TITLE        = {On three generalizations of contraction},
   YEAR         = {2014},
   OPTADDRESS   = {},
   OPTCROSSREF  = {},
   OPTEDITOR    = {},
   OPTMONTH     = {},
   OPTNOTE      = {},
   OPTNUMBER    = {},
   OPTORGANIZATION = {},
   PAGES        = {1539-1544},
   OPTPUBLISHER = {},
   OPTSERIES    = {},
   OPTVOLUME    = {},
   KEYWORDS     = {contractions, contractive systems, stability},
   ABSTRACT     = {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.}
}

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