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.ss 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 that

U_list = [ U_i sqrt(hsv_i) ] VT_list = [ sqrt(hsv_i) V_i.T ]

where U_i and V_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.

Frequency-Limited Balanced ROMs may be obtained from SHARPy using sharpy.rom.balanced.FrequencyLimited.