# On Fixed Points of Strictly Causal Functions

## THIS REPORT HAS BEEN WITHDRAWN

### Eleftherios Matsikoudis and Edward A. Lee

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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.