ml_dt_ss_adtf
Additive decomposition of standard system's transfer function.
Contents
Syntax
[sys, info] = ml_dt_ss_adtf(sys) [sys, info] = ml_dt_ss_adtf(sys, opts)
Description
Consider a standard discrete-time system of the form
x(t+1) = A*x(t) + B*u(t), (1) y(t) = C*x(t). (2)
This function computes an additive decomposition of the corresponding transfer function by a block diagonalization of the matrix A. The system is transformed, such that
[ As ] [ Bs ] z(t+1) = [ ]z(t) + [ ]u(t), (3) [ Au ] [ Bu ]
y(t) = [ Cs, Cu ]z(t), (4)
where As contains the eigenvalues with absolute values smaller than 1 and Au all the eigenvalues with absolute values larger than 1.
Input
- sys - structure, containing the descriptor system in the form:
Parameter | Meaning |
A | matrix with dimensions n x n in (1) |
B | matrix with dimensions n x m in (1) |
C | matrix with dimensions p x n in (2) |
- opts - structure, containing the following optional entries:
Parameter | Meaning |
stabsignmopts | structure, containing the optional parameters for the matrix sign function used for the decomposition into stable and anti-stable system parts, see ml_signm default: struct() |
stabdsylvopts | structure, containing the optional parameters for the Sylvester equation solver used for the decomposition into stable and anti-stable system parts, see ml_dsylv_smith default: struct() |
StoreProjection | {0, 1}, used to disable/enable storing of the computed projection matrices W and T default: 0 |
UnstabDim | integer, dimension of the deflating anti-stable subspace, negative if unknown default: -1 |
Output
- sys - structure, containing the transformed descriptor system:
Parameter | Meaning |
A | matrix with dimensions ns x ns, see As in (3) |
Au | matrix with dimensions nu x nu in (3) |
B | matrix with dimensions ns x m, see Bs in (3) |
Bu | matrix with dimensions nu x m in (3) |
C | matrix with dimensions p x ns, see Cs in (4) |
Cu | matrix with dimensions p x nu in (4) |
- info - structure, containing the following information about the algorithms used for the additive decomposition
Entry | Meaning |
infoSTABSIGNM | structure, containing information about the matrix sign function method, see ml_signm |
infoSTABDSYLV | structure, containing information about the Sylvester equation solver, see ml_dsylv_sgn |
Ns | Number of identified stable eigenvalues |
Nu | Number of identified anti-stable eigenvalues |
T | projection matrix used as right state-space transformation to obtain the resulting block system, if opts.StoreProjection == 1 |
W | projection matrix used as left state-space transformation to obtain the resulting block system, if opts.StoreProjection == 1 |
Reference
S. Werner, Hankel-norm approximation of descriptor systems, Master's thesis, Otto von Guericke University, Magdeburg, Germany (2016). http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-8845
See Also