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 (Robust Control Toolbox), uss (Robust Control Toolbox), or ufrd (Robust Control Toolbox) 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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