ml_lyapdl_sgn_fac

Continuous-time dual 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

   A*X  + X*A' + B*B' = 0,                                         (1)
   A'*Y + Y*A  + C'*C = 0,                                         (2)

or of the dual generalized Lyapunov equations

   A*X*E' + E*X*A' + B*B' = 0,                                     (3)
   A'*Y*E + E'*Y*A + 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

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

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

ml_lyapdl_sgn_ldl | ml_lyap_sgn_fac