|Title||Algebraic approach to the computation of the defining polynomial of the algebraic Riccati equation.|
|Author(s)|| Kitamoto Takuya|
|Type||Book, Chapter in Book, Conference Proceeding|
|Abstract||The algebraic Riccati equation, which we denote by ’ARE’ in the rest of the paper, is one of the most important equations of the post modern control theory. It plays important role for solving H 2 and H  ∞  optimal control problems.|
Although a well-known numerical algorithm can compute the solution of ARE efficiently (,) the algorithm can not be applied when a given system contains an unknown parameter.
This paper presents an algorithm to compute the defining polynomial of an ARE with unknown parameter k. Such algorithm is also discussed in , where an algorithm with numerical approach is presented. The new algorithm in this paper uses algebraic approaches based on Groebner basis and resultant. Numerical experiments show the new algorithm is more efficient than that of  in most cases.