Calculates an LTI Frequency Response Function
H = ltifrf(A,B,C,,,w,outopt)
H = ltifrf(A,B,C,D,,w,outopt)
H = ltifrf(,,,D,,w,outopt)
H = ltifrf(A,B,C,,dA,w,outopt)
ltifrf will return the Frequency Response Function (FRF) of a linear time-invariant state-space model, evaluated at the complex frequencies provided in w:
A is the state-space model matrix A.
B is the state-space model matrix B.
C is the state-space model matrix C.
D is the (optional) state-space model matrix D.
dA (optional) calculates the change in FRF given the deviation dA in A. D and dA are mutually exclusive.
w is the vector of complex frequencies. For discrete-time systems:
and for continuous-time systems.
outopt controls how H will be returned (see below).
H is the FRF. Usually a 3D-array of size l x m x N. However, if outopt is non-empty and 1, H will be a vector of size lmN x 1. If outopt is non-empty and 2, H will be a matrix of size l x mN.
The state-space model is first transformed such that its state-transistion matrix A is in upper-Hessenberg form. The matrix
is subsequently solved by an efficient upper-Hessenberg solver in SLICOT, after which premultiplication by C and addition of D yields the FRF. This approach follows .
If a deviation deltaA in A is given, the FRF deviation is given by:
Again, the model is transformed so that A has upper-Hessenberg form, after which the SLICOT Hessenberg solver is used to obtain
Multiplication then yeilds the FRF deviation.
SLICOT-functions MB02RZ, MB02SZ, TB05AD
LAPACK-functions DGEHRD and DORMHR
(All built into the executable)
 A.J. Laub, "Efficient multivariable frequency response calculations", IEEE Transactions on Automatic Control, vol. 26, pp. 407-408, Apr. 1981.