Linear systems with sign-observations. Koplon, R. & Sontag, E. SIAM J. Control Optim., 31(5):1245–1266, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1993.
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This paper deals with systems that are obtained from linear time-invariant continuous- or discrete-time devices followed by a function that just provides the sign of each output. Such systems appear naturally in the study of quantized observations as well as in signal processing and neural network theory. Results are given on observability, minimal realizations, and other system-theoretic concepts. Certain major differences exist with the linear case, and other results generalize in a surprisingly straightforward manner.
@ARTICLE{MR1234002,
   AUTHOR       = {R. Koplon and E.D. Sontag},
   JOURNAL      = {SIAM J. Control Optim.},
   TITLE        = {Linear systems with sign-observations},
   YEAR         = {1993},
   OPTMONTH     = {},
   OPTNOTE      = {},
   NUMBER       = {5},
   PAGES        = {1245--1266},
   VOLUME       = {31},
   ADDRESS      = {Philadelphia, PA, USA},
   KEYWORDS     = {observability},
   PUBLISHER    = {Society for Industrial and Applied Mathematics},
   PDF          = {../../FTPDIR/signlinear_koplon_sontag_repreint_siam1993.pdf},
   ABSTRACT     = { This paper deals with systems that are obtained from 
      linear time-invariant continuous- or discrete-time devices followed 
      by a function that just provides the sign of each output. Such 
      systems appear naturally in the study of quantized observations as 
      well as in signal processing and neural network theory. Results are 
      given on observability, minimal realizations, and other 
      system-theoretic concepts. Certain major differences exist with the 
      linear case, and other results generalize in a surprisingly 
      straightforward manner. },
   DOI          = {http://dx.doi.org/10.1137/0331059}
}

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