linear fractional transformation
S = lft(P, R) [S, s] = lft(P, p, R) [S, s] = lft(P, p, R, r)
linear system (in state space or transfer function representation) or a simple gain, the ``augmented'' plant, implicitly partitioned into four blocks (two input ports and two output ports).
1x2 row vector, the dimensions of the P_22
block (see below).
llinear system (in state space or transfer function representation) or a simple gain, implicitly partitioned into four blocks (two input ports and two output ports).
1x2 row vector, dimension of the
R_22
block . This argument should not
be used. It is retained for compatibility with
previous versions.
linear system, the linear fractional transform.
1x2 row vector, dimension of the S_22
block (see below).
Linear fractional transform between two standard plants in state space form or in transfer form:
S=lft(P,R)
Computes the linear fractional transform between the
systems P
and a controller
R
. The system S
corresponds to the transfer
if ny
and nu
are
respectively the number of inputs and outputs of
R
, one must have
size(P)>=[ny nu]
.
The system returned is formally equivalent to
i1 = 1:($-ny);j1=1:($-nu); i2 = ($-ny+1):$;j1=($-nu+1):$; S = P(i1,j1) + P(i1,j2) * R * (eye() - P(i2,j2) * R) \P(i2,j1) | ![]() | ![]() |
lft
instead of the code above avoids numerical problems and non
minimal realization.[S,s]=lft(P,p,R)
with p= [ny,nu]
Forms the
generalized (2 ports) lft of P
and
R
.
S
is the two-port interconnected
plant, which correspond to the transfer:
s
is the dimension of the
22
block of S
.
P
and R
can be PSSDs i.e. may admit a
polynomial D
matrix.