The Fixed-Point Theory of Strictly Causal Functions
Abstract
We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a xed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding xed-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 xed-point theorem for these functions, introduce a corresponding induction principle, and study the related convergence process.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 09, 2013
- Accession Number
- ADA586605
Entities
People
- Edward A. Lee
- Eleftherios Matsikoudis
Organizations
- University of California, Berkeley