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TitleParametric polynomial spectral factorization using the sum of roots and its application to a control design problem
Author(s) Hirokazu Anai, Shinji Hara, Masaaki Kanno, Kazuhiro Yokoyama
TypeArticle in Journal
AbstractThis paper presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Gröbner bases and polynomial spectral factorization which can be observed through the sum of roots, and allows us to perform polynomial spectral factorization in the presence of real parameters. It is discussed that parametric polynomial spectral factorization enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs two quantifier elimination techniques. This proposed approach is demonstrated in a numerical example of a particular control problem.
KeywordsSum of roots, Parametric polynomial spectral factorization, Parametric optimization, Gröbner basis, Quantifier elimination, H 2 control
URL http://www.sciencedirect.com/science/article/pii/S0747717108001181
JournalJournal of Symbolic Computation
Pages703 - 725
NoteInternational Symposium on Symbolic and Algebraic Computation
Translation No
Refereed No