ml_lyapdl_sgn_ldl

Dual continuous-time Lyapunov equation solver.

Contents

Syntax

[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, [], C, [])
[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, Q, C, R)
[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, Q, C, R, [])
[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, Q, C, R, [], opts)
[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, [], C, [], E)
[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, Q, C, R, E)
[RZ, RY, LZ, LY, info] = ml_lyapdl_sgn_ldl(A, B, Q, C, R, E, opts)

Description

Computes the full-rank solutions of the dual standard Lyapunov
equations
    AX1  + X1A' + BQB' = 0,                                         (1)
    A'X2 + X2A  + C'RC = 0,                                         (2)
or of the dual generalized Lyapunov equations
    AX1E' + EX1A' + BQB' = 0,                                       (3)
    A'X2E + E'X2A + C'RC = 0,                                       (4)
with X1 = RZ'*RY*RZ and X2 = LZ'*LY*LZ, 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)
Q    - symmetric matrix with dimensions m x m in (1) or (3), if empty
       Q is assumed to be the identity
C    - matrix with dimensions p x n in (2) or (4)
R    - symmetric matrix with dimensions p x p in (2) or (4), if empty
       R is assumed to be the identity
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: 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

RZ   - full-rank solution factor of (1) or (3), s.t. X1 = RZ'*RY*RZ
RY   - full-rank solution factor of (1) or (3), s.t. X1 = RZ'*RY*RZ
LZ   - full-rank solution factor of (2) or (4), s.t. X2 = LZ'*LY*LZ
LY   - full-rank solution factor of (2) or (4), s.t. X2 = LZ'*LY*LZ
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

See Also

ml_lyapdl_sgn_fac | ml_lyap_sgn_ldl