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

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)

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()
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

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)

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
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

ml_ct_dss_adtf | ml_ss_lti2struct