Solution of algebraic riccati equations using the sum of roots

Authors:
Masaaki Kanno;Kazuhiro Yokoyama;Hirokazu Anai;Shinji Hara
Affiliations:
Niigata University, Niigata, Japan;Rikkyo University, Tokyo, Japan;Fujitsu Laboratories Ltd, Kawasaki, Japan;The University of Tokyo, Tokyo, Japan
Venue:
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Year:
2009

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Abstract

This paper constructs an algebraic solution approach to the algebraic Riccati equation, an important equation in signal processing and control system design. Key features of the proposed approach are the exploitation of useful structures inherent in the problem and the avoidance of Gröbner basis computation by generic algorithms. The approach extends the algebraic approach to polynomial spectral factorization by means of the Sum of Roots. The approach further finds an effective symbolic expression of the eigenvector of the associated Hamiltonian matrix in a simple way. An example is presented to demonstrate the proposed algorithm.