Title :
A method for solving the algebraic Riccati and Lyapunov equations using higher order matrix sign function algorithms
Author :
Hasan, Mohammed A. ; Hasan, Ali A.
Author_Institution :
Dept. of Comput. Eng., Minnesota Univ., Duluth, MN, USA
Abstract :
Higher order iterations for computing the matrix sign function of complex matrices are developed in this paper. The technique of generating higher order fixed point function produces the Newton and Halley methods as special cases for solving the equations S2=I, and such that SA=AS has all its eigenvalues in the right halfplane. The matrix sign function is used to compute the positive semidefinite solution of the algebraic Riccati and Lyapunov matrix equations. The performance of these methods is demonstrated by several examples
Keywords :
Lyapunov matrix equations; Newton method; Riccati equations; eigenvalues and eigenfunctions; Halley method; Lyapunov equation; Newton method; algebraic Riccati equation; eigenvalues; higher order matrix; matrix sign function; Approximation methods; Control theory; Differential algebraic equations; Eigenvalues and eigenfunctions; Riccati equations; Signal processing; Signal processing algorithms; Symmetric matrices;
Conference_Titel :
Decision and Control, 1998. Proceedings of the 37th IEEE Conference on
Conference_Location :
Tampa, FL
Print_ISBN :
0-7803-4394-8
DOI :
10.1109/CDC.1998.762009
