ml_ct_ss_adtf

Additive decomposition of standard system's transfer function.

Contents

Syntax

[sys, info] = ml_ct_ss_adtf(sys)
[sys, info] = ml_ct_ss_adtf(sys, opts)

Description

Consider a standard system of the form
    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 A. The
system is transformed, such that
            [ As     ]       [ Bs ]
    z'(t) = [        ]z(t) + [    ]u(t),                            (3)
            [     Au ]       [ Bu ]
    y(t)  = [ Cs, Cu ]z(t),                                         (4)
where As contains the eigenvalues with negative real parts and Au all
the eigenvalues with positive real parts.

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()
stabsylvopts
structure, containing the optional parameters for the Sylvester equation solver used for the decomposition into stable and anti-stable system parts, see ml_sylv_sgn
default: struct()
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
infoSTABSYLV
structure, containing information about the Sylvester equation solver, see ml_sylv_sgn
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_dss_adtf | ml_ct_ss_lti2struct