ml_sylv_sgn_fac
Continuous-time factorized Sylvester equation solver.
Contents
Syntax
[X, info] = ml_sylv_sgn_fac(A, B, G, H) [X, info] = ml_sylv_sgn_fac(A, B, G, H, []) [X, info] = ml_sylv_sgn_fac(A, B, G, H, [], []) [X, info] = ml_sylv_sgn_fac(A, B, G, H, [], [], opts)
[X, info] = ml_sylv_sgn_fac(A, B, G, H, E, F) [X, info] = ml_sylv_sgn_fac(A, B, G, H, E, F, opts)
Description
Computes the solution matrix of the standard factorized Sylvester equation
A*X + X*B + G*H = 0, (1)
or of the generalized factorized Sylvester equation
A*X*F + E*X*B + G*H = 0, (2)
where the solution is given as X = Y*Z, using the sign function iteration. It is assumed that the eigenvalues of A and B (or s*E - A and s*F - 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)
- G - matrix with dimensions n x p from (1) or (2)
- H - matrix with dimensions p x m from (1) or (2)
- E - matrix with dimensions n x n from (2), if empty it is assumed to be the identity
- F - matrix with dimensions m x m 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 |
CompTol | nonnegative scalar, tolerance for the row compression during the iteration default: sqrt(n)*eps |
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
- Y - solution factor of the Sylvester equation (1) or (2), such that X = Y*Z
- Z - solution factor of the Sylvester equation (1) or (2), such that X = Y*Z
- 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