Accession Number:

ADA586605

Title:

The Fixed-Point Theory of Strictly Causal Functions

Descriptive Note:

Technical rept.

Corporate Author:

CALIFORNIA UNIV BERKELEY DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Report Date:

2013-06-09

Pagination or Media Count:

68.0

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.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE