This paper is concerned with linear networks dependingpolynomially on parameters, when considering large values of theparameters, and their corresponding ideal networks--i.e. the networksin which all parameters are set equal to infinity. It has been takeninto account that only the specification of nominal values andtolerances--and not of actual values--is physically meaningful. Thestability of the ideal networks and the least hypotheses that allowus to use a previous algorithm to find monomial functions--in asingle suitable variable--that describe arbitrarily large nominalvalues which ensure stability within a suitable constant toleranceare assumed. An integer h such that while these nominal values go toinfinity then for any smooth causal excitations bounded together withtheir first h derivatives--in particular, for any smooth eventuallyperiodic causal excitations--the zero-state response of the actualnetworks converges uniformly on the whole time axis to that of theideal networks is proved to exist. The proof may be used as analgorithm. An example which proves that the found class ofexcitations may be not the widest is given. The application of theresults to the evaluation of the synchronization error due to highbut finite values of the parameters in an ideally synchronizinglinear network is shown. Copyright
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