B = imp2exp(A,yidx,uidx)
transforms a linear constraint between variables y and
u of the form A(:,[yidx;uidx])*[y;u] = 0 into an
explicit input/output relationship y = B*u. The vectors
yidx and uidx refer to the columns (inputs) of
A as referenced by the explicit relationship for
B.

Consider two uncertain motor/generator constraints among 4 variables $$\left[\begin{array}{c}V\\ I\\ T\\ W\end{array}\right]$$, namely $$\left[\begin{array}{cccc}1& -R& 0& -K\\ 0& -K& 1& 0\end{array}\right]*\left[\begin{array}{c}V\\ I\\ T\\ W\end{array}\right]=0$$. Find the uncertain 2-by-2 matrix B so that $$\left[\begin{array}{c}V\\ T\end{array}\right]=B*\left[\begin{array}{c}W\\ I\end{array}\right]$$.

R = ureal('R',1,'Percentage',[-10 40]);
K = ureal('K',2e-3,'Percentage',[-30 30]);
A = [1 -R 0 -K;0 -K 1 0];
Yidx = [1 3];
Uidx = [4 2];
B = imp2exp(A,Yidx,Uidx)

B =
Uncertain matrix with 2 rows and 2 columns.
The uncertainty consists of the following blocks:
K: Uncertain real, nominal = 0.002, variability = [-30,30]%, 2 occurrences
R: Uncertain real, nominal = 1, variability = [-10,40]%, 1 occurrences
Type "B.NominalValue" to see the nominal value, "get(B)" to see all properties, and "B.Uncertainty" to interact with the uncertain elements.

Consider a standard single-loop feedback connection of controller C and an uncertain plant P, described by the equations e = r-y; u = Ce; f = d+u; y = Pf.

A — Implicit system static or dynamic input/output model

Implicit system, specified as a static, or dynamic input/output model.
A can be:

A numeric LTI model such as tf, zpk, ss, or frd object

An uncertain model such as umat, uss, or ufrd object

The number of rows in model A must equal the length of the
index vector yidx.

yidx — Indices to partition implicit model channels into output signals vector

Indices to partition the model channel into output signals, specified as a vector.
The index vectors yidx and uidx specify how to
partition the input channels of A into y and
u signals, respectively.

If [yidx,uidx] does not include all inputs of
A, imp2exp excludes the missing
y channels from the output model B. In such
cases, imp2exp retains only a subset B(I,:) of the
outputs/rows of B and does not affect how the explicit model
B is computed.

uidx — Indices to partition implicit model channels into input signals vector

Indices to partition the model channel into input signals, specified as a vector.
The index vectors yidx and uidx specify how to
partition the input channels of A into y and
u signals, respectively.

B — Explicit system static or dynamic input/output model

Explicit system, returned as a static, or dynamic input/output model. The output
explicit model B is of the same subclass as model
A. For instance, if A is specified as an
ss model, then imp2exp also returns
B as an ss model.

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