ml_lyap_sgn_ldl
Continuous-time Lyapunov equation solver.
Contents
Syntax
[Z, info] = ml_lyap_sgn_ldl(A, C) [Z, info] = ml_lyap_sgn_ldl(A, C, R) [Z, info] = ml_lyap_sgn_ldl(A, C, R, []) [Z, info] = ml_lyap_sgn_ldl(A, C, R, [], opts)
[Z, info] = ml_lyap_sgn_ldl(A, C, R, E) [Z, info] = ml_lyap_sgn_ldl(A, C, R, E, opts)
Description
Computes the full-rank solution of the standard Lyapunov equation
A'X + XA + C'RC = 0, (1)
or of the generalized Lyapunov equation
A'XE + E'XA + C'RC = 0, (2)
with X = Z'*Y*Z, 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) or (2) C - matrix with dimensions p x n in (1) or (2) R - symmetric matrix with dimensions p x p in (1) or (2), if empty R is assumed to be the identity E - matrix with dimensions n x n in (2), if empty the standard equation (1) is 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 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
Z - full-rank solution factor of (1) or (2), such that X = Z'*Y*Z Y - full-rank solution factor of (1) or (2), such that X = Z'*Y*Z 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