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Properties and Classification of Generalized Resultants and Polynomial Combinants

Karcanias, N. (2013). Properties and Classification of Generalized Resultants and Polynomial Combinants. 2013 21st Mediterranean Conference on Control & Automation (MED), pp. 788-793. doi: 10.1109/MED.2013.6608813


Polynomial combinants define the linear part of the Dynamic Determinantal Assignment Problems, which provides the unifying description of the frequency assignment problems in Linear Systems. The theory of dynamic polynomial combinants have been recently developed by examining issues of their representation, parameterization of dynamic polynomial combinants according to the notions of order and degree and spectral assignment. Dynamic combinants are linked to the theory of “Generalised Resultants”, which provide the matrix representation of polynomial combinants. We consider coprime set polynomials for which assignability is always feasible and provides a complete characterisation of all assignable combinants with order above and below the Sylvester order. The complete parameterization of combinants and coresponding Generalised Resultants is prerequisite to the characterisation of the minimal degree and order combinant for which spectrum assignability may be achieved.

Publication Type: Article
Additional Information: © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Engineering
School of Science & Technology > Engineering > Electrical & Electronic Engineering
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