ml_lyapdl_sgn
Continuous-time dual Lyapunov equation solver.
Contents
Syntax
[X, Y, info] = ml_lyapdl_sgn(A, Q, R) [X, Y, info] = ml_lyapdl_sgn(A, Q, R, []) [X, Y, info] = ml_lyapdl_sgn(A, Q, R, [], opts)
[X, Y, info] = ml_lyapdl_sgn(A, Q, R, E) [X, Y, info] = ml_lyapdl_sgn(A, Q, R, E, opts)
Description
Computes the solutions of the dual standard Lyapunov equations
A*X + X*A' + Q = 0, (1) A'*Y + Y*A + R = 0, (2)
or of the dual generalized Lyapunov equations
A*X*E' + E*X*A' + Q = 0, (4) A'*Y*E + E'*Y*A + R = 0, (3)
with X = R'*R and Y = L'*L, using the sign function iteration. It is assumed that the eigenvalues of A (or s*E - A) lie in the open left half-plane.
Input
- A - matrix with dimensions n x n in (1), (2) or (3), (4)
- Q - matrix with dimensions n x n in (1) or (3)
- R - matrix with dimensions n x n in (2) or (4)
- E - matrix with dimensions n x n in (3), (4), if empty the standard equations (1), (2) are solved
- 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 (1) or (3)
- Y - solution of (2) or (4)
- 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, J. M. Claver, E. S. Quintana-Orti, Efficient solution of coupled Lyapunov equations via matrix sign function iteration, in: Proc. 3rd Portuguese Conf. on Automatic Control CONTROLO'98, Coimbra, 1998, pp. 205--210.
See Also