Improved results on frequency-weighted balanced truncation and error bounds

In this paper, we present some new results on frequency-weighted balanced truncation which is a significant improvement on Lin and Chiu's frequency-weighted balanced truncation technique. The reduced-order models, which are guaranteed to be stable in the case of double-sided weighting, are obtained by direct truncation. Two sets of simple, elegant and easily calculatable a priori error bounds are also derived. Numerical examples and comparison with other well-known techniques show the effectiveness of the proposed technique

Model reduction based on limited time interval impulse response gramians

— This paper presents a new limited time interval impulse response Gramians (LTIRG) based model reduction method for single-input single-output (SISO) continuous-time systems. The proposed approach incorporates the time-interval Gramians with impulse response Gramians to preserve the input-output behaviour of the original system for the specified time interval. A numerical example is given to illustrate the proposed approach, and the results are compared with the standard techniques