On the Generalized Numerical Range.
| dc.contributor.author | Fan, Michael K-H. | en_US |
| dc.contributor.author | Tits, A.L. | en_US |
| dc.contributor.department | ISR | en_US |
| dc.date.accessioned | 2007-05-23T09:35:43Z | |
| dc.date.available | 2007-05-23T09:35:43Z | |
| dc.date.issued | 1986 | en_US |
| dc.description.abstract | Let A_k, k = 1, ...., m be n x n Hermitian matricies and let f: C^n --> R^m have components f^k(x) = x^H A_k(x), k = 1, ..., m. When n >= 3 and m = 3, the set W(A_1>,..., A_m) = {f(x): || x || = 1} PROPER subset of R_m is convex. This property does not hold in general when m > 3. These particuar cases of known results are proven here using a direct, geometric approach. A geometric characterization of the contact surfaces is obtained for any n and m. Necessary conditions are given for f(x) to be on boundary of W(A_1,..., A_2) or on the certain subsets of this boundary. These results are of interest in the context of the computations of the structured singular value, a recently introduced tool for the analysis and synthesis of control systems. | en_US |
| dc.format.extent | 299587 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/4482 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | ISR; TR 1986-57 | en_US |
| dc.title | On the Generalized Numerical Range. | en_US |
| dc.type | Technical Report | en_US |
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