On fixed points of strictly causal functions

  • Authors:
  • Eleftherios Matsikoudis;Edward A. Lee

  • Affiliations:
  • University of California, Berkeley;University of California, Berkeley

  • Venue:
  • FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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.