In this work, we present a new cross-gramian. The proposed gramian is a truncated gramian which supports bilinear systems. It is proven that the truncated cross-gramian can be obtained by solving ordinary Sylvester equation. It is computationally less expensive to compute the truncated cross-gramian compared to the standard cross-gramians which are solutions to the generalized Sylvester equations. A projection based model reduction method is proposed based upon the truncated crossgramian. The proposed method is among the first cross-gramian based methods - if not the only one- which is developed for bilinear systems. This model reduction is computationally more efficient than model reduction techniques which are derived from standard gramains or the truncated controllability and observability gramians.
|Title of host publication||2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI)|
|Number of pages||5|
|Publication status||Published - 2021|
|Event||2021 International Conference on Recent Advances in Mathematics and Informatics - Tebessa, Algeria|
Duration: 21 Sep 2021 → 22 Sep 2021
|Conference||2021 International Conference on Recent Advances in Mathematics and Informatics|
|Period||21/09/2021 → 22/09/2021|