ml_caredl_sgn
Continuous-time Riccati equation solver.
Contents
Syntax
[X, Y, info] = ml_caredl_sgn(A, B, C) [X, Y, info] = ml_caredl_sgn(A, B, C, []) [X, Y, info] = ml_caredl_sgn(A, B, C, [], opts)
[X, Y, info] = ml_caredl_sgn(A, B, C, E) [X, Y, info] = ml_caredl_sgn(A, B, C, E, opts)
Description
Computes the solution matrix of the standard dual algebraic Riccati equations
A'X + XA - XBB'X + C'C = 0, (1) AY + YA' - YC'CY + BB' = 0, (2)
or of the generalized dual Riccati equations
A'XE + E'XA - E'XBB'XE + C'C = 0, (3) AYE' + EYA' - EYC'CYE' + BB' = 0, (4)
using the factored sign function iteration. It is assumed that A (and E) is invertible.
Input
A - matrix with dimensions n x n in (1), (2) or (3), (4) B - matrix with dimensions n x m in (1), (2) or (3), (4) C - matrix with dimensions p x n in (1), (2) or (3), (4) E - matrix with dimensions n x n in (3), (4), 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 and column compression during the iteration default: 1.0e-02*sqrt(n*eps) |
EqnType | character array, switch for only computing the solution of one type of the above equations
|
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
X - solution matrix of (1) or (2) info - structure, containing the following information:
Entry | Meaning |
AbsErr | vector, containing the absolute change of the iteration matrix in each iteration step |
IterationSteps | number of performed iteration steps |
RelErr | vector, containing the relative change of the iteration matrix in each iteration step |
Reference
P. Benner, P. Ezzatti, E. S. Quintana-Orti, A. Remon, A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function, Numer. Algorithms 66 (2) (2014) 363--377. https://doi.org/10.1007/s11075-013-9739-2
See Also