An infinite-time relaxation theorem for differential inclusions. Ingalls, B., Sontag, E., & Wang, Y. Proc. Amer. Math. Soc., 131(2):487–499, 2003.
abstract   bibtex   
The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.
@ARTICLE{relaxation-DE-PAMS03,
   AUTHOR       = {B.P. Ingalls and E.D. Sontag and Y. Wang},
   JOURNAL      = {Proc. Amer. Math. Soc.},
   TITLE        = {An infinite-time relaxation theorem for differential 
      inclusions},
   YEAR         = {2003},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {2},
   PAGES        = {487--499},
   VOLUME       = {131},
   PDF          = {../../FTPDIR/relaxation-di-as-appeared.pdf},
   ABSTRACT     = { The fundamental relaxation result for Lipschitz 
      differential inclusions is the Filippov-Wazewski Relaxation Theorem, 
      which provides approximations of trajectories of a relaxed inclusion 
      on finite intervals. A complementary result is presented, which 
      provides approximations on infinite intervals, but does not guarantee 
      that the approximation and the reference trajectory satisfy the same 
      initial condition. }
}

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