Citation
Eleftherios Matsikoudis, Edward A. Lee. "On Fixed Points of Strictly Causal Functions". 11th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS), Buenos Aires, Argentina, 29, August, 2013.

Abstract
We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive fixed-point theorem for these functions, and introduce a corresponding induction principle.

Electronic downloads

• http://dx.doi.org/10.1007/978-3-642-40229-6_13

• HTML

  Eleftherios Matsikoudis, Edward A. Lee. <a
  href="http://chess.eecs.berkeley.edu/pubs/996.html"
  >On Fixed Points of Strictly Causal Functions</a>,
  11th International Conference on Formal Modeling and
  Analysis of Timed Systems (FORMATS), Buenos Aires,
  Argentina, 29, August, 2013.

• Plain text

  Eleftherios Matsikoudis, Edward A. Lee. "On Fixed
  Points of Strictly Causal Functions". 11th
  International Conference on Formal Modeling and Analysis of
  Timed Systems (FORMATS), Buenos Aires, Argentina, 29,
  August, 2013.

• BibTeX

  @inproceedings{MatsikoudisLee13_OnFixedPointsOfStrictlyCausalFunctions,
      author = {Eleftherios Matsikoudis and Edward A. Lee},
      title = {On Fixed Points of Strictly Causal Functions},
      booktitle = {11th International Conference on Formal Modeling
                and Analysis of Timed Systems (FORMATS), Buenos
                Aires, Argentina},
      day = {29},
      month = {August},
      year = {2013},
      abstract = {We ask whether strictly causal components form
                well defined systems when arranged in feedback
                configurations. The standard interpretation for
                such configurations induces a fixed-point
                constraint on the function modelling the component
                involved. We define strictly causal functions
                formally, and show that the corresponding
                fixed-point problem does not always have a well
                defined solution. We examine the relationship
                between these functions and the functions that are
                strictly contracting with respect to a generalized
                distance function on signals, and argue that these
                strictly contracting functions are actually the
                functions that one ought to be interested in. We
                prove a constructive fixed-point theorem for these
                functions, and introduce a corresponding induction
                principle.},
      URL = {http://chess.eecs.berkeley.edu/pubs/996.html}
  }
  

Posted by Eleftherios Matsikoudis on 26 Jun 2013.
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