1 Department of Energy Technology, The Faculty of Engineering and Science, Aalborg University, VBN2 Fluid Power and Mechatronic Systems, The Faculty of Engineering and Science, Aalborg University, VBN3 The Faculty of Engineering and Science (ENG), Aalborg University, VBN
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.
Proceedings of the 7th Ieee Conference on Industrial Electronics and Applications (iciea), 2012, p. 749-751
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7th IEEE Conference on Industrial Electronics and Applications, 2012