ml_lyapdl_sgn_ldl
Continuous-time dual 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
A*X1 + X1*A' + B*Q*B' = 0, (1) A'*X2 + X2*A + C'*R*C = 0, (2)
or of the dual generalized Lyapunov equations
A*X1*E' + E*X1*A' + B*Q*B' = 0, (3) A'*X2*E + E'*X2*A + C'*R*C = 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