Optimal choice of time-scaling factor for linear systemapproximations using Laguerre models

摘要

Clowes (1965) illustrated how to select the optimal time-scaling factor for approximations of rational transfer functions using a series expansion of Laguerre functions. The present paper extends this result to approximations for general, L2 stable, linear systems. As a direct application of this extended result, we are able to obtain approximations for irrational transfer functions which minimize the frequency domain error in the L2 sense. Also, we give empirical solutions for the optimal time-scaling factor for approximations of first order plus delay systems which can then be applied to a larger class of overdamped systems