Error bound for transfer function order reduction using freqeuncy weighted balanced truncation

Abstract

An error bound for transfer function order reduction is derived, when frequency weighted balanced truncation is the order reduction method. The bound is valid for both one-sided (input or output) and two-sided weighted balancing approximations with stable weights, which can otherwise be arbitrary. The error bound formula is valid for both discrete-time and continuous-time problems. Examples are studied to demonstrate effectiveness of the error bound. Show more