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A symplectic QR like algorithm for the solution of the real algebraic Riccati equation

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2 Author(s)
Bunse-Gerstner, A. ; Universität Bielefeld, Bielefeld, West Germany ; Mehrmann, V.

A method is presented to solve the real algebraic Riccati equation - XNX + XA + A^{T}X + K = 0 , where K = K^{T} and N = N^{T} . The solution for the corresponding eigenvalue problem Mx = \lambda x , where M is a Hamiltonian matrix, is computed by an algorithm similar to the QR algorithm. Special symplectic matrices are used for the transformation of M such that the Hamiltonian form is preserved during the computations.

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Automatic Control, IEEE Transactions on  (Volume:31 ,  Issue: 12 )