ml_sylv_sgn

Continuous-time Sylvester equation solver.

Contents

Syntax

[X, info] = ml_sylv_sgn(A, B, C)
[X, info] = ml_sylv_sgn(A, B, C, [])
[X, info] = ml_sylv_sgn(A, B, C, [], [])
[X, info] = ml_sylv_sgn(A, B, C, [], [], opts)
[X, info] = ml_sylv_sgn(A, B, C, E, F)
[X, info] = ml_sylv_sgn(A, B, C, E, F, opts)

Description

Computes the solution matrix of the standard Sylvester equation
    AX + XB = C,                                                    (1)
or of the generalized Sylvester equation
    A*X*E + F*X*B = C,                                              (2)
using the sign function iteration. It is assumed that the eigenvalues
of A and B (or s*F - A and s*E - B) lie in the open left half-plane.

Input

A    - matrix with dimensions n x n from (1) or (2)
B    - matrix with dimensions m x m from (1) or (2)
C    - matrix with dimensions n x m from (1) or (2)
E    - matrix with dimensions m x m from (2), if empty it is assumed to
       be the identity
F    - matrix with dimensions n x n from (2), if empty it is assumed to
       be the identity
opts - structure, containing the following optional entries:

Parameter
Meaning
AbsTol
nonnegative scalar, tolerance for the absolute error in the last iteration step
default: 0
Info
{0, 1}, used to disable/enable display of verbose status information during iteration steps
default: 0
MaxIter
positive integer, maximum number of iteration steps
default: 100
RelTol
nonnegative scalar, tolerance for the relative error in the last iteration step
default: 1.0e+01*n*eps

Output

X    - solution of the Sylvester equation (1) or (2)
info - structure, containing the following information:

Entry
Meaning
AbsErr
vector, containing the absolute error of the iteration matrix in each iteration step
IterationSteps
number of performed iteration steps
RelErr
vector, containing the relative error of the iteration matrix in each iteration step

Reference

P. Benner, Factorized solution of Sylvester equations with applications in control, in: Proc. Intl. Symp. Math. Theory Networks and Syst. MTNS 2004, 2004

See Also

ml_lyap_sgn | ml_abe_sgn