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Linear networks depending polynomially on parameters: dynamic behaviour for large values subject to tolerance errors
Author(s) -
Ciampa Maurizio,
Poletti Mario
Publication year - 1999
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199909/10)27:5<497::aid-cta77>3.0.co;2-8
Subject(s) - ideal (ethics) , bounded function , mathematics , synchronizing , constant (computer programming) , stability (learning theory) , monomial , infinity , class (philosophy) , synchronization (alternating current) , set (abstract data type) , zero (linguistics) , discrete mathematics , computer science , topology (electrical circuits) , mathematical analysis , combinatorics , philosophy , linguistics , epistemology , machine learning , artificial intelligence , programming language
This paper is concerned with linear networks depending polynomially on parameters, when considering large values of the parameters, and their corresponding ideal networks—i.e. the networks in which all parameters are set equal to infinity. It has been taken into account that only the specification of nominal values and tolerances—and not of actual values—is physically meaningful. The stability of the ideal networks and the least hypotheses that allow us to use a previous algorithm to find monomial functions—in a single suitable variable—that describe arbitrarily large nominal values which ensure stability within a suitable constant tolerance are assumed. An integer h such that while these nominal values go to infinity then for any smooth causal excitations bounded together with their first h derivatives—in particular, for any smooth eventually periodic causal excitations—the zero‐state response of the actual networks converges uniformly on the whole time axis to that of the ideal networks is proved to exist. The proof may be used as an algorithm. An example which proves that the found class of excitations may be not the widest is given. The application of the results to the evaluation of the synchronization error due to high but finite values of the parameters in an ideally synchronizing linear network is shown. Copyright © 1999 John Wiley & Sons, Ltd.