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   ]
    [    Einf    ]z'(t) = [     Ainf     ]z(t) + [ Binf ]u(t),      (3)
    [         Eu ]        [           Au ]       [ Bu   ]
                   y(t) = [ Cf, Cinf, Cu ]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 disk function and subspace extraction method, see ml_disk, ml_getqz
default: struct()
stabdecopts
structure, containing the optional parameters for the decomposition of the stable and unstable parts of the system using the disk function and subspace extraction method, see ml_disk, ml_getqz
default: struct()

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
infoSTABDISK
structure, containing information about the disk function method used for the separation of the unstable part, see ml_disk
Ninf
Number of identified infinite eigenvalues
Ns
Number of identified stable eigenvalues
Nu
Number of identified anti-stable eigenvalues

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

ml_ct_ss_adtf | ml_ct_dss_lti2struct