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严格因果功能中的定点理论

The Fixed-Point Theory of Strictly Causal Functions
作者:Eleftherios Matsikoudis;Edward A. Lee; 作者单位:Electrical Engineering and Computer Sciences 加工时间:2013-11-08 信息来源:EECS 索取原文[66 页]
关键词:严格因果分量;反馈配置;定点理论;函数
摘 要:We ask whether strictly causal components form well de ned systems when arranged in feedback con gurations. The standard interpretation for such con gurations induces a xed-point constraint on the function modelling the component involved. We de ne strictly causal functions formally, and show that the corresponding xed-point problem does not always have a well de ned 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.
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