On the relationship between the sum of roots with positive real parts and polynomial spectral factorization

Authors:
Masaaki Kanno;Hirokazu Anai;Kazuhiro Yokoyama
Affiliations:
CREST, Japan Science and Technology Agency, Kawaguchi-shi, Saitama, Japan;Fujitsu Laboratories Ltd, CREST JST, Kawasaki, Japan;Rikkyo University, CREST JST, Tokyo, Japan
Venue:
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Year:
2006

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Abstract

This paper is concerned with the relationship between the sum of roots with positive real parts (SORPRP) of an even polynomial and the polynomial spectral factor of the even polynomial. The SORPRP and its relationship to Gröbner bases are firstly reviewed. Then it is shown that the system of equations satisfied by the coefficients of the polynomial spectral factor is directly related to a Gröbner basis. It is then demonstrated by means of an H2 optimal control problem that the above fact can be used to facilitate guaranteed accuracy computation.