摘要
The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt&rarr0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has been reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae = eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.
The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt&rarr0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has been reduced from the original 2n-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation Ae = eA. All the eigenvalues of Ae are in the unit circle, with the eigenvectors unchanged and the original eigenvalues can be obtained by a logarithm operation. And several of the eigenvalues of Ae nearest to the unit circle can be calculated by the dual subspace iteration method.
