@INPROCEEDINGS{02mtns-relaxation,
   AUTHOR       = {B.P. Ingalls and E.D. Sontag and Y. Wang},
   BOOKTITLE    = {Mathematical Theory of Networks and Systems, Electronic Proceedings of MTNS-2002 Symposium held at the University of Notre Dame, August 2002},
   TITLE        = {A relaxation theorem for differential inclusions with 
      applications to stability properties},
   YEAR         = {2002},
   OPTADDRESS   = {},
   OPTCROSSREF  = {},
   EDITOR       = {D. Gilliam and J. Rosenthal},
   OPTMONTH     = {},
   NOTE         = {(12 pages)},
   OPTNUMBER    = {},
   OPTORGANIZATION = {},
   OPTPAGES     = {},
   OPTPUBLISHER = {},
   OPTSERIES    = {},
   OPTVOLUME    = {},
   PDF          = {../../FTPDIR/02mtns-ingalls-sontag-wang.pdf},
   ABSTRACT     = { The fundamental Filippov--Wazwski Relaxation Theorem 
      states that the solution set of an initial value problem for a 
      locally Lipschitz inclusion is dense in the solution set of the same 
      initial value problem for the corresponding relaxation inclusion on 
      compact intervals. In a recent paper of ours, a complementary result 
      was provided for inclusions with finite dimensional state spaces 
      which says that the approximation can be carried out over non-compact 
      or infinite intervals provided one does not insist on the same 
      initial values. This note extends the infinite-time relaxation 
      theorem to the inclusions whose state spaces are Banach spaces. To 
      illustrate the motivations for studying such approximation results, 
      we briefly discuss a quick application of the result to output 
      stability and uniform output stability properties. }
}

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