Linear networks depending polynomially on parameters: Dynamic behaviour for large values subject to tolerance errors

This paper is concerned with linear networks depending polynomially on para meters, when considering large values of the parameters, and their correspo nding ideal networks-i.e. the networks in which all parameters are set equa l to infinity. It has been taken into account that only the specification o f nominal values and tolerances-and not of actual values-is physically mean ingful. 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 stabi lity within a suitable constant tolerance are assumed. An integer h such that while these nominal values go to infinity then for a ny smooth causal excitations bounded together with their first h derivative s-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 sy nchronization error due to high but finite values of the parameters in an i deally synchronizing linear network is shown. Copyright (C) 1999 John Wiley & Sons, Ltd.