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

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, L/sub 2/ 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 L/sub 2/ 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.<
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