A new method for computing the closed-loop eigenvalues of a discrete-time algebraic Riccati equation

Abstract We present a fast method for computing the closed-loop eigenvalues of a discrete-time algebraic Riccati equation. The method is close to the symplectic method for finding all the eigenvalues of a Hamiltonian matrix and is based on a (Γ, ΓG)-orthogonal transformation, which preserves structure and has desirable numerical properties. The algorithm requires about one-fourth the number of floating-point operations and one-half the storage of the QZ algorithm.

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