FLB_transfer_function
Returns an interpolatory state-space model based on the transfer function method [1]. This method is applicable to frequency limited balanced state-space models only.
Features:
stability preserved
the interpolated state-space model has the same size than the tabulated ones
all state-space models, need to have the same size and the same numbers of hankel singular values.
suitable for any ROM
- param SS_list:
List of state-space models instances of
sharpy.linear.src.libss.StateSpace
class.- type SS_list:
list
- param wv:
list of interpolatory weights.
- type wv:
list
- param U_list:
small size, thin SVD factors of Gramians square roots of each state space model (\(\mathbf{U}\)).
- type U_list:
list
- param VT_list:
small size, thin SVD factors of Gramians square roots of each state space model (\(\mathbf{V}^\top\)).
- type VT_list:
list
- param hsv_list:
small size, thin SVD factors of Gramians square roots of each state space model. If
None
, it is assumed thatU_list = [ U_i sqrt(hsv_i) ]
VT_list = [ sqrt(hsv_i) V_i.T ]
where
U_i
andV_i.T
are square matrices and hsv is an array.- type hsv_list:
list
- param M_list:
for fast on-line evaluation. Small size product of Gramians factors of each state-space model. Each element of this list is equal to:
M_i = U_i hsv_i V_i.T
- type M_list:
list
Notes
Message for future generations:
the implementation is divided into an offline and online part.
References:
Maraniello S. and Palacios R., Frequency-limited balanced truncation for parametric reduced-order modelling of the UVLM. Only in the best theaters.
See also
Frequency-Limited Balanced ROMs may be obtained from SHARPy using sharpy.rom.balanced.FrequencyLimited
.