关键词: linear quadratic control, eigenvalue, eigenvector, eigen-pairs

Abstract: The degeneration of the eigenvalue equation of the discrete-time linear quadratic control problem to the continuous-time one when Δt→0 is given first. When the continuous-time n-dimensional eigenvalue equation, which has all the eigenvalues located in the left half plane, has bee ft reduced from the original In-dimensional one, the present paper proposes that several of the eigenvalues nearest to the imaginary axis be obtained by the matrix transformation A_e=e^A.All the eigenvalues of A_e 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 A_e nearest to the unit circle can be calculated by the dual subspace iteration method.

Key words: linear quadratic control, eigenvalue, eigenvector, eigen-pairs