ml_lyapdl_sgn_fac
Dual continuous-time Lyapunov equation solver.
Contents
Syntax
[R, L, info] = ml_lyapdl_sgn_fac(A, B, C) [R, L, info] = ml_lyapdl_sgn_fac(A, B, C, []) [R, L, info] = ml_lyapdl_sgn_fac(A, B, C, [], opts)
[R, L, info] = ml_lyapdl_sgn_fac(A, B, C, E) [R, L, info] = ml_lyapdl_sgn_fac(A, B, C, E, opts)
Description
Computes the full-rank solutions of the dual standard Lyapunov equations
AX + XA' + BB' = 0, (1) A'Y + YA + C'C = 0, (2)
or of the dual generalized Lyapunov equations
AXE' + EXA' + BB' = 0, (3) A'YE + E'YA + C'C = 0, (4)
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) B - matrix with dimensions n x m in (1) or (3) C - matrix with dimensions p 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 |
CompTol | nonnegative scalar, tolerance for the column and row compression during the iteration default: 1.0e-02*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
R - full-rank solution factor of (1), such that X = R'*R L - full-rank solution factor of (2), such that Y = L'*L 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