ml_ss_sr
Square root method for standard systems.
Contents
Syntax
[sys, hsv, T, W] = ml_ss_sr(sys, R, L, tselect) [sys, hsv, T, W] = ml_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 = S^(-1/2) * U' * L', 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 n x nr
- L - Cholesky factor of the observability Gramian with dimensions n x nl
- 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 default: Inf |
Order {!} | positive integer, order of the resulting reduced-order model chosen by the user if tselect == 1 default: min(10,length(hsv)) + nu |
StoreProjection | {0, 1}, used to disable/enable storing of the computed projection matrices W and T default: 0 |
Tolerance {!} | nonnegative scalar, tolerance used in the different error formulas default: 1.0e-02 |
Note: Parameters marked with {!} may also be a cell array containing multiple arguments. In this case an cell array of the same size is returned with one entry computed for each input argument and the marked fields of the info struct are cells as well. When multiple arguments are given as cells, they are expected to have the same length.
Output
- sys - struct, containing the transformed system matrices
- hsv - vector, containing the characteristic singular values
- T - right projection matrix, if opts.StoreProjection == 1
- W - left projection matrix, if opts.StoreProjection == 1
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