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


Personal Author(s) : Matsikoudis, Eleftherios ; Lee, Edward A


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a586605.pdf


Report Date : 09 Jun 2013


Pagination or Media Count : 68


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.


Descriptors :   *FUNCTIONS(MATHEMATICS) , CONFIGURATIONS


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE