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On Fixed Points of Strictly Causal Functions

  • Eleftherios Matsikoudis
  • Edward A. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8053)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Eleftherios Matsikoudis
    • 1
  • Edward A. Lee
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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