Solution of algebraic riccati equations using the sum of roots
Masaaki Kanno, Kazuhiro Yokoyama, Hirokazu Anai, Shinji Hara · 2009
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.