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 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.
Title
The Fixed-Point Theory of Strictly Causal Functions
Published
2013-06-09
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2013-122
Type
Text
Extent
67 p
Archive
The Engineering Library
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