ml_ct_ss_sr
Square root method for standard systems.
Contents
Syntax
[sys, hsv] = ml_ct_ss_sr(sys, R, L, tselect) [sys, hsv] = ml_ct_ss_sr(sys, R, L, tselect, opts)
Description
Computes the reduced-order matrices of a standard system by the square root method. Therefore, transformation matrices of the form
W = L * U * S^(-1/2), T = R * V * S^(-1/2)
are computed, where U, S, V result from singular value decompositions. The computation of the reduced-order model is done by
Ar = W' * A * T,
Br = W' * B,
Cr = C * T.
Input
sys - structure, containing the standard system in the form:
Parameter | Meaning |
A | matrix with dimensions n x n |
B | matrix with dimensions n x m |
C | matrix with dimensions p x n |
R - Cholesky factor of the controllability Gramian with dimensions nr x n L - Cholesky factor of the observability Gramian with dimensions nl x n tselect - an integer, used to determine the computation method for the order of the reduced-order model 0 - order is directly given by user 1 - computed by a relative tolerance for the hsv 2 - computed by a relative tolerance on the sum of hsv 3 - computed by absolute error bound of BT 4 - computed by relative error bound of BST 5 - computed by absolute error bound of LQGBT 6 - computed by absolute error bound of HinfBT opts - structure, containing the following optional entries:
Parameter | Meaning |
Gamma | positive scalar, scaling term from the H-infinity balanced truncation |
Order | positive integer, order of the resulting reduced-order model chosen by the user if tselect == 1 default: min(10,length(hsvp))+nu |
Tolerance | nonnegative scalar, tolerance used in the different error formulas default: 1.0e-02 |
Output
sys - struct, containing the transformed system matrices hsv - vector, containing the characteristic singular values
Reference
A. Varga, Controller reduction using accuracy-enhancing methods, in: P. Benner, V. Mehrmann, D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Vol. 45 of Lect. Notes Comput. Sci. Eng., Springer-Verlag, Berlin/Heidelberg, Germany, 2005, pp. 353--356. https://doi.org/10.1007/3-540-27909-1_9
See Also