On the computation of the main eigen-pairs of the continuous-time linear quadratic control problem

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 beeh 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 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.