Abstract
The cross-gramian is a well-known matrix with
embedded controllability and observability information. The
cross-gramian is related to the Hankel operator and the Hankel
singular values of a linear square system and it has several
interesting properties. These properties make the cross-gramian
popular in several applications including model reduction, control
configuration selection and sensitivity analysis. The ordinary
cross-gramian which has been defined in the literature is the
solution of a Sylvester equation. This Sylvester equation is not
always solvable and therefore for some linear square symmetric
systems, the ordinary cross-gramian does not exist. To cope with
this problem, a new generalized cross-gramian is introduced
in this paper. In contrast to the ordinary cross-gramian, the
generalized cross-gramian can be easily obtained for general
linear systems and therefore can be used in the applications
instead of the ordinary cross-gramian.
embedded controllability and observability information. The
cross-gramian is related to the Hankel operator and the Hankel
singular values of a linear square system and it has several
interesting properties. These properties make the cross-gramian
popular in several applications including model reduction, control
configuration selection and sensitivity analysis. The ordinary
cross-gramian which has been defined in the literature is the
solution of a Sylvester equation. This Sylvester equation is not
always solvable and therefore for some linear square symmetric
systems, the ordinary cross-gramian does not exist. To cope with
this problem, a new generalized cross-gramian is introduced
in this paper. In contrast to the ordinary cross-gramian, the
generalized cross-gramian can be easily obtained for general
linear systems and therefore can be used in the applications
instead of the ordinary cross-gramian.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) |
| Number of pages | 3 |
| Publisher | IEEE Press |
| Publication date | 2012 |
| Pages | 749-751 |
| ISBN (Print) | 978-1-4577-2118-2 |
| ISBN (Electronic) | 978-1-4577-2117-5 |
| DOIs | |
| Publication status | Published - 2012 |
| Event | 7th IEEE Conference on Industrial Electronics and Applications : ICIEA 2012 - , Singapore Duration: 18 Jul 2012 → 20 Jul 2012 |
Conference
| Conference | 7th IEEE Conference on Industrial Electronics and Applications |
|---|---|
| Country/Territory | Singapore |
| Period | 18/07/2012 → 20/07/2012 |