Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-29T14:08:14.483Z Has data issue: false hasContentIssue false
  • English
  • Français

On the square-root method for continuous-time algebraic Riccati equations

Published online by Cambridge University Press:  17 February 2009

Linzhang Lu  and
C. E. M. Pearce
Linzhang Lu
Affiliation:
Mathematics Department, Xiamen University, Fujian, P. R., China
C. E. M. Pearce
Affiliation:
Applied Mathematics Department, Adelaide University, Adelaide SA 5005, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a simple and transparent proof for the square-root method of solving the continuous-time algebraic Riccati equation. We examine some benefits of combining the square-root method with other solution methods. The iterative square-root method is also discussed. Finally, paradigm numerical examples are given to compare the square-root method with the Schur method.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 4 , April 1999 , pp. 459 - 468
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Byers, R., “Hamiltonian and symplectic algorithms for algebraic Riccati equations”, Ph. D. Thesis, Cornell Univ., Ithaca, NY, 1982.Google Scholar
[2]Denman, D. and Beavers, A. N., “The matrix sign function and computation in systems”, Appl. Math. Comput. 2 (1976) 63–94.Google Scholar
[3]Gantmacher, F. R., The theory of matrices (Chelsea, New York, 1959).Google Scholar
[4]Hoskins, W. D. and Walton, D. J., “A faster method of computing the square root of a matrix”, IEEE Trans. Automat. Control 23 (1978) 494–495.CrossRefGoogle Scholar
[5]Laub, A. J., “A schur method for solving algebraic Riccati equations”, IEEE Trans. Automat. Control 24 (1979) 913–921.CrossRefGoogle Scholar
[6]Lu, Linzhang, “On sign function and square root methods for solution of real algebraic Riccati equations”, Numer. Math., J. Chinese Univ. 1 (1992) 81–90.Google Scholar
[7]Lu, Linzhang and Lin, Wenwei, “An iterative algorithm for the solution of the discrete-time algebraic Riccati equation”, Lin. Alg. Appl. 188–189 (1993) 465–488.CrossRefGoogle Scholar
[8]van Loan, C. F., “A symplectic method for approximating all eigenvalues of a Hamiltonian matrix”, Lin. Alg. Appl. 61 (1984) 233–251.CrossRefGoogle Scholar
[9]Xu, Hongguo and Lu, Linzhang, “Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation”, Lin. Alg. Appl. 222 (1995) 127–145.CrossRefGoogle Scholar