Balanced truncation with relative/multiplicative error bounds in L ∞ norm

Studies a class of balanced truncation algorithms applicable to relative/multiplicative model reduction. These algorithms seek to balance the controllability gramian of a given transfer function and the observability gramian of its right inverse. For this reason, the algorithms are referred to as inverse-weighted balanced truncation (IWBT) algorithms. It is shown that by using IWBT algorithms one can derive relative and multiplicative L_∞ error bounds that are known to hold for other reduction algorithms. It is also shown that the balanced stochastic truncation (BST) method is actually one special, but an “optimal” version of the IWBT algorithms. As such, the authors´ result also serves to establish the fact that the available error bounds pertaining to BST algorithms actually hold for IWBT algorithms