ml_ct_ss_mt
Modal truncation for standard systems.
Contents
Syntax
[Ar, Br, Cr, Dr, info] = ml_ct_ss_mt(A, B, C, D) [Ar, Br, Cr, Dr, info] = ml_ct_ss_mt(A, B, C, D, opts)
[rom, info] = ml_ct_ss_mt(sys) [rom, info] = ml_ct_ss_mt(sys, opts)
Description
This function computes the modal truncation for a standard system of the form
x'(t) = A*x(t) + B*u(t), (1) y(t) = C*x(t) + D*u(t). (2)
Therefore, a block diagonalization of the matrix A is performed using the matrix sign function and a Sylvester equation, such that
[ Ar 0 ] [ Cr ] A2 = [ ], B2 = [ Br, B1 ], C2 = [ ], Dr = D, [ 0 A1 ] [ C1 ]
where Ar contains all the eigenvalues of A, which have a larger real part than a given alpha. As result, the reduced-order system is given by
x'(t) = Ar*x(t) + Br*u(t), (3) y(t) = Cr*x(t) + Dr*u(t). (4)
Input
A - matrix from (1) with dimensions n x n B - matrix from (1) with dimensions n x m C - matrix from (2) with dimensions p x n D - matrix from (2) with dimensions p x m sys - structure or state-space object, containing the standard system's matrices:
Entry | Meaning |
A | matrix from (1) with dimensions n x n |
B | matrix from (1) with dimensions n x m |
C | matrix from (2) with dimensions p x n |
D | matrix from (2) with dimensions p x m |
opts - structure, containing the following optional entries:
Parameter | Meaning |
Alpha | scalar, such that all finite eigenvalues with the real part smaller than Alpha are truncated default: -1.0 |
signmopts | structure, containing the optional parameters for the matrix sign function used for the decomposition of the eigenvalues, see ml_signm default: struct() |
sylvopts | structure, containing the optional parameters for the Sylvester equation solver used for the decomposition of the eigenvalues, see ml_sylv_sgn default: struct() |
Output
Ar - matrix of (3) with dimensions r x r Br - matrix of (3) with dimensions r x m Cr - matrix of (4) with dimensions p x r Dr - matrix of (4) with dimensions p x m rom - structure or state-space object, with the following entries:
Entry | Meaning |
A | matrix from (3) with dimensions r x r |
B | matrix from (3) with dimensions r x m |
C | matrix from (4) with dimensions p x r |
D | matrix from (4) with dimensions p x m |
info - structure, containing the following information:
Entry | Meaning |
infoSIGNM | structure, containing information about the matrix sign function method, see ml_signm |
infoSYLV | structure, containing information about the Sylvester equation solver, see ml_sylv_sgn |
N | Dimension of the reduced-order model |
Reference
P. Benner, E. S. Quintana-Orti, Model reduction based on spectral projection methods, in: P. Benner, V. Mehrmann, D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Vol. 45 of Lect. Notes Comput. Sci. Eng., Springer, Berlin/Heidelberg, Germany, 2005, pp. 5--45. https://doi.org/10.1007/3-540-27909-1_1
See Also