Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences


UC Berkeley

On Fixed Points of Strictly Causal Functions


Eleftherios Matsikoudis and Edward A. Lee

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2013-27
April 8, 2013

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 tagged 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, introduce a corresponding induction principle, and study the related convergence process.