Applied Mathematics and Mechanics (English Edition) ›› 1991, Vol. 12 ›› Issue (1): 49-54.

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ON THE COMPUTATION OF THE MAIN EIGEN-PAIRS OF THE CONTINUOUS-TIME LINEAR QUADRATIC CONTROL PROBLEM

Zhong Wan-xie1, Yang Zai-shi2   

  1. 1. Dalian University of Technology, Dalian. Shanghai Jiaotong University, Shanghai; Winning Software Corporation;
    2. Higher Education Press, Beijing
  • Received:1990-01-15 Online:1991-01-18 Published:1991-01-18

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 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.

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

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