Input-to-state stability with respect to inputs and their derivatives. Angeli, D., Sontag, E., & Wang, Y. Internat. J. Robust Nonlinear Control, 13(11):1035–1056, 2003.
abstract   bibtex   
A new notion of input-to-state stability involving infinity norms of input derivatives up to a finite order k is introduced and characterized. An example shows that this notion of stability is indeed weaker than the usual ISS. Applications to the study of global asymptotic stability of cascaded nonlinear systems are discussed.
@ARTICLE{DiffISS_IJRNC03,
   AUTHOR       = {D. Angeli and E.D. Sontag and Y. Wang},
   JOURNAL      = {Internat. J. Robust Nonlinear Control},
   TITLE        = {Input-to-state stability with respect to inputs and 
      their derivatives},
   YEAR         = {2003},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {11},
   PAGES        = {1035--1056},
   VOLUME       = {13},
   KEYWORDS     = {input to state stability, input to state stability},
   PDF          = {../../FTPDIR/diss-ijrac03.pdf},
   ABSTRACT     = { A new notion of input-to-state stability involving 
      infinity norms of input derivatives up to a finite order k is 
      introduced and characterized. An example shows that this notion of 
      stability is indeed weaker than the usual ISS. Applications to the 
      study of global asymptotic stability of cascaded nonlinear systems 
      are discussed. }
}

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