DocumentCode :
343304
Title :
A method for solving the algebraic Riccati and Lyapunov equations using higher order matrix sign function algorithms
Author :
Hasan, Mohammed A. ; Yang, Jiann-Shiou ; Hasan, Ali A.
Author_Institution :
Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN, USA
Volume :
4
fYear :
1999
fDate :
1999
Firstpage :
2345
Abstract :
A set of higher order rational fixed point functions for computing the matrix sign function of complex matrices is developed. Our main focus is the representation of these rational functions in partial fraction form which in turn allows for a parallel implementation of the matrix sign function algorithms. The matrix sign function is then used to compute the positive semidefinite solution of the algebraic Riccati and Lyapunov matrix equations. It is also suggested that the proposed methods can be used to compute the invariant subspaces of a nonsingular matrix in any half plane. The performance of these methods is demonstrated by several examples
Keywords :
Lyapunov matrix equations; Riccati equations; rational functions; Lyapunov matrix equations; algebraic Riccati equation; higher order matrix sign function algorithms; higher order rational fixed point functions; invariant subspaces; nonsingular matrix; partial fraction form; positive semidefinite solution; Approximation methods; Concurrent computing; Control theory; Educational institutions; Eigenvalues and eigenfunctions; Polynomials; Riccati equations;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
American Control Conference, 1999. Proceedings of the 1999
Conference_Location :
San Diego, CA
ISSN :
0743-1619
Print_ISBN :
0-7803-4990-3
Type :
conf
DOI :
10.1109/ACC.1999.786463
Filename :
786463
Link To Document :
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