ml_ct_dss_adtf
Add. decomposition of descriptor system's transfer function.
Contents
Syntax
[sys, info] = ml_ct_dss_adtf(sys) [sys, info] = ml_ct_dss_adtf(sys, opts)
Description
Consider a descriptor system of the form
E*x'(t) = 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 pencil s*E - A. The descriptor system is transformed, such that
[ Ef ] [ Af ] [ Bf ] [ Eu ]z'(t) = [ Au ]z(t) + [ Bu ]u(t), (3) [ Einf ] [ Ainf ] [ Binf ]
y(t) = [ Cf, Cu, Cinf ]z(t), (4)
where s*Ef - Af contains the finite eigenvalues with negative real parts, s*Einf - Ainf the infinite eigenvalues and s*Eu - Au the finite eigenvalues with positive real parts.
Input
- sys - structure, containing the descriptor system in the form:
Parameter | Meaning |
E | matrix with dimensions n x n in (1) |
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 |
DecompEig | positive scalar, overestimation of the absolute value of the largest finite eigenvalue of s*E - A, if set, replaces the computation with DecompTol default: [] |
DecompTol | nonnegative scalar, tolerance multiplied with the largest singular value of E to determine the smallest non-zero singular value of E default: log(n)*eps |
infdecopts | structure, containing the optional parameters for the decomposition of the finite and infinite parts of the system using the sign function and subspace extraction method, see ml_disk and ml_getqz default: struct() |
stabdecopts | structure, containing the optional parameters for the decomposition of the stable and unstable parts of the system using the sign function and subspace extraction method, see ml_signm and ml_getqz default: struct() |
StoreProjection | {0, 1}, used to disable/enable storing of the computed projection matrices W and T default: 0 |
Output
- sys - structure, containing the transformed descriptor system:
Parameter | Meaning |
E | matrix with dimensions nf x nf, see Ef in (3) |
Einf | matrix with dimensions ninf x ninf in (3) |
Eu | matrix with dimensions nu x nu in (3) |
A | matrix with dimensions nf x nf, see Af in (3) |
Ainf | matrix with dimensions ninf x ninf in (3) |
Au | matrix with dimensions nu x nu in (3) |
B | matrix with dimensions nf x m, see Bf in (3) |
Binf | matrix with dimensions ninf x m in (3) |
Bu | matrix with dimensions nu x m in (3) |
C | matrix with dimensions p x nf, see Cf in (4) |
Cinf | matrix with dimensions p x ninf in (4) |
Cu | matrix with dimensions p x nu in (4) |
- info - structure, containing the following information about the additive decomposition of the descriptor system
Entry | Meaning |
infoINFDISK | structure, containing information about the disk function method used for the separation of the infinite part, see ml_disk |
infoSTABSIGNM | structure, containing information about the sign function method used for the separation of the unstable part, see ml_signm |
Ninf | Number of identified infinite eigenvalues |
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