Input-output-to-state stability. Krichman, M., Sontag, E., & Wang, Y. SIAM J. Control Optim., 39(6):1874–1928, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001.
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This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of "norm-estimators", and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.
@ARTICLE{krichman_sontag_wang_IOSS_01,
   AUTHOR       = {M. Krichman and E.D. Sontag and Y. Wang},
   JOURNAL      = {SIAM J. Control Optim.},
   TITLE        = {Input-output-to-state stability},
   YEAR         = {2001},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {6},
   PAGES        = {1874--1928},
   VOLUME       = {39},
   ADDRESS      = {Philadelphia, PA, USA},
   KEYWORDS     = {input to state stability},
   PUBLISHER    = {Society for Industrial and Applied Mathematics},
   PDF          = {../../FTPDIR/ioss_input_output_to_state_krichman_sontag_wang_reprint_siam2001.pdf},
   ABSTRACT     = { This work explores Lyapunov characterizations of the 
      input-output-to-state stability (IOSS) property for nonlinear 
      systems. The notion of IOSS is a natural generalization of the 
      standard zero-detectability property used in the linear case. The 
      main contribution of this work is to establish a complete equivalence 
      between the input-output-to-state stability property and the 
      existence of a certain type of smooth Lyapunov function. As 
      corollaries, one shows the existence of "norm-estimators", and 
      obtains characterizations of nonlinear detectability in terms of 
      relative stability and of finite-energy estimates. },
   DOI          = {http://dx.doi.org/10.1137/S0363012999365352}
}

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